# Fusc sequence

The   fusc   integer sequence is defined as:

Definitions
•   fusc(0) = 0
•   fusc(1) = 1
•   for n>1,   the   nth   term is defined as:
•   if   n   is even;     fusc(n) = fusc(n/2)
•   if   n   is   odd;     fusc(n) = fusc((n-1)/2)   +   fusc((n+1)/2)

Note that MathWorld's definition starts with unity, not zero.   This task will be using the OEIS' version   (above).

An observation
•   fusc(A) = fusc(B)

where   A   is some non-negative integer expressed in binary,   and where   B   is the binary value of   A   reversed.

Fusc numbers are also known as:

•   fusc function   (named by Dijkstra, 1982)
•   Stern's Diatomic series   (although it starts with unity, not zero)
•   Stern-Brocot sequence   (although it starts with unity, not zero)

•   show the first   61   fusc numbers (starting at zero) in a horizontal format.
•   show the fusc number (and its index) whose length is greater than any previous fusc number length.
•   (the length is the number of decimal digits when the fusc number is expressed in base ten.)
•   show all numbers with commas   (if appropriate).
•   show all output here.

Also see

## 11l

Translation of: Kotlin
```F fusc(n)
V res =  * n
res = 1
L(i) 2 .< n
res[i] = I i % 2 == 0 {res[i I/ 2]} E res[(i-1) I/ 2] + res[(i+1) I/ 2]
R res

print(‘First 61 terms:’)
print(fusc(61))

print()
print(‘Points in the sequence where an item has more digits than any previous items:’)
V f = fusc(20'000'000)
V max_len = 0
L(i) 0 .< f.len
I String(f[i]).len > max_len
max_len = String(f[i]).len
print((i, f[i]))```
Output:
```First 61 terms:
[0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4]

Points in the sequence where an item has more digits than any previous items:
(0, 0)
(37, 11)
(1173, 108)
(35499, 1076)
(699051, 10946)
(19573419, 103682)
```

```with Ada.Text_IO;

procedure Show_Fusc is

generic
Precalculate : Natural;
package Fusc_Sequences is
function Fusc (N : in Natural) return Natural;
end Fusc_Sequences;

package body Fusc_Sequences is

Precalculated_Fusc : array (0 .. Precalculate) of Natural;

function Fusc_Slow (N : in Natural) return Natural is
begin
if N = 0 or N = 1 then
return N;
elsif N mod 2 = 0 then
return Fusc_Slow (N / 2);
else
return Fusc_Slow ((N - 1) / 2) + Fusc_Slow ((N + 1) / 2);
end if;
end Fusc_Slow;

function Fusc (N : in Natural) return Natural is
begin
if N <= Precalculate then
return Precalculated_Fusc (N);
elsif N mod 2 = 0 then
return Fusc (N / 2);
else
return Fusc ((N - 1) / 2) + Fusc ((N + 1) / 2);
end if;
end Fusc;

begin
for N in Precalculated_Fusc'Range loop
Precalculated_Fusc (N) := Fusc_Slow (N);
end loop;
end Fusc_Sequences;

package Fusc_Sequence is
new Fusc_Sequences (Precalculate => 200_000);

function Fusc (N : in Natural) return Natural
renames Fusc_Sequence.Fusc;

procedure Print_Small_Fuscs is
begin
Put_Line ("First 61 numbers in the fusc sequence:");
for N in 0 .. 60 loop
Put (Fusc (N)'Image);
Put (" ");
end loop;
New_Line;
end Print_Small_Fuscs;

procedure Print_Large_Fuscs (High : in Natural) is
subtype N_Range is Natural range Natural'First .. High;
F       : Natural;
Len     : Natural;
Max_Len : Natural := 0;
Placeholder : String := "       n      fusc(n)";
Image_N     : String renames Placeholder (1  .. 8);
Image_Fusc  : String renames Placeholder (10 .. Placeholder'Last);
begin
New_Line;
Put_Line ("Printing all largest Fusc numbers upto " & High'Image);
Put_Line (Placeholder);

for N in N_Range loop
F   := Fusc (N);
Len := F'Image'Length;

if Len > Max_Len then
Max_Len := Len;
Put (Image_N,    N);
Put (Image_Fusc, F);
Put (Placeholder);
New_Line;
end if;
end loop;
end Print_Large_Fuscs;

begin
Print_Small_Fuscs;
Print_Large_Fuscs (High => 20_000_000);
end Show_Fusc;
```
Output:
```First 61 numbers in the fusc sequence:
0  1  1  2  1  3  2  3  1  4  3  5  2  5  3  4  1  5  4  7  3  8  5  7  2  7  5  8  3  7  4  5  1  6  5  9  4  11  7  10  3  11  8  13  5  12  7  9  2  9  7  12  5  13  8  11  3  10  7  11  4

Printing all largest Fusc numbers upto  20000000
n      fusc(n)
0            0
37           11
1173          108
35499         1076
699051        10946
19573419       103682```

## ALGOL 68

```BEGIN
# calculate some members of the fusc sequence              #
#    f0 = 0, f1 = 1, fn = f(n/2)                 if n even #
#                       = f(n-1)/2) + f((n+1)/2) if n odd  #

# constructs an array of the first n elements of the fusc sequence #
PROC fusc sequence = ( INT n )[]INT:
BEGIN
[ 0 : n ]INT a;
IF n > 0 THEN
a[ 0 ] := 0;
IF n > 1 THEN
a[ 1 ] := 1;
INT i2 := 1;
FOR i FROM 2 BY 2 TO n - 1 DO
a[ i     ] := a[ i2 ];
a[ i + 1 ] := a[ # j - i # i2 ] + a[ # ( j + 1 ) OVER 2 # i2 + 1 ];
i2 +:= 1
OD
FI
FI;
a[ 0 : n - 1 AT 0 ]
END ; # fusc #

[]INT f = fusc sequence( 800 000 );
FOR i FROM 0 TO 60 DO print( ( " ", whole( f[ i ], 0 ) ) ) OD;
print( ( newline ) );
# find the lowest elements of the sequence that have 1, 2, 3, etc. digits #
print( ( "Sequence elements where number of digits of the value increase:", newline ) );
print( ( "       n    fusc(n)", newline ) );
INT digit power := 0;
FOR i FROM LWB f TO UPB f DO
IF f[ i ] >= digit power THEN
# found the first number with this many digits #
print( ( whole( i, -8 ), " ", whole( f[ i ], -10 ), newline ) );
IF digit power = 0 THEN digit power := 1 FI;
digit power *:= 10
FI
OD
END```
Output:
``` 0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
Sequence elements where number of digits of the value increase:
n    fusc(n)
0          0
37         11
1173        108
35499       1076
699051      10946
```

## AppleScript

```on fusc(n)
if (n < 2) then
return n
else if (n mod 2 is 0) then
return fusc(n div 2)
else
return fusc((n - 1) div 2) + fusc((n + 1) div 2)
end if
end fusc

set sequence to {}
set longestSoFar to 0
repeat with i from 0 to 60
set fuscNumber to fusc(i)
set end of sequence to fuscNumber
set len to (count (fuscNumber as text))
if (len > longestSoFar) then
set longestSoFar to len
set firstLongest to fuscNumber
set indexThereof to i + 1 -- AppleScript indices are 1-based.
end if
end repeat

return {sequence:sequence, firstLongest:firstLongest, indexThereof:indexThereof}
```
Output:
`{sequence:{0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4}, firstLongest:11, indexThereof:38}`

Or defining generators, both for a non-finite stream of Fusc terms, and for the sequence of the first Fusc terms of each decimal magnitude:

```-- fusc :: [Int]
on fusc()
-- Terms of the Fusc sequence
-- OEIS A2487

script go
on |λ|(step)
set {isEven, n, xxs} to step
set x to item 1 of xxs

if isEven then
set nxt to n + x
{not isEven, nxt, xxs & {nxt}}
else
{not isEven, x, rest of xxs & {x}}
end if
end |λ|
end script

appendGen(gen({0, 1}), ¬
fmapGen(my snd, iterate(go, {true, 1, {1}})))
end fusc

-------------------------- TEST ---------------------------
on run
unlines({¬
"First 61 terms:", ¬
showList(take(61, fusc())), ¬
"", ¬
"First term of each decimal magnitude:", ¬
"(Index, Term):"} & ¬
map(showTuple, take(4, firstFuscOfEachMagnitude())))
end run

---------- FIRST FUSC OF EACH DECIMAL MAGNITUDE -----------

-- firstFuscOfEachMagnitude :: [(Int, Int)]
on firstFuscOfEachMagnitude()
-- [(Index, Term)] list of of the first Fusc
-- terms of each decimal magnitude.
script
property e : -1
property i : 0
on |λ|()
set e to 1 + e
set p to 10 ^ e
set v to fuscTerm(i)
repeat until p ≤ v
set i to 1 + i
set v to fuscTerm(i)
end repeat
{i, v}
end |λ|
end script
end firstFuscOfEachMagnitude

-- fuscTerm :: Int -> Int
on fuscTerm(n)
-- Nth term (zero-indexed) of the Fusc series.
script go
on |λ|(i)
if 0 = i then
{1, 0}
else
set {x, y} to |λ|(i div 2)
if 0 = i mod 2 then
{x + y, y}
else
{x, x + y}
end if
end if
end |λ|
end script

tell go
if 1 > n then
0
else
item 1 of |λ|(n - 1)
end if
end tell
end fuscTerm

-------------------- GENERIC FUNCTIONS --------------------

-- appendGen (++) :: Gen [a] -> Gen [a] -> Gen [a]
on appendGen(xs, ys)
script
property vs : xs
on |λ|()
set v to |λ|() of vs
if missing value is not v then
v
else
set vs to ys
|λ|() of ys
end if
end |λ|
end script
end appendGen

-- fmapGen <\$> :: (a -> b) -> Gen [a] -> Gen [b]
on fmapGen(f, gen)
script
property g : mReturn(f)
on |λ|()
set v to gen's |λ|()
if v is missing value then
v
else
g's |λ|(v)
end if
end |λ|
end script
end fmapGen

-- intercalate :: String -> [String] -> String
on intercalate(delim, xs)
set {dlm, my text item delimiters} to ¬
{my text item delimiters, delim}
set s to xs as text
set my text item delimiters to dlm
s
end intercalate

-- iterate :: (a -> a) -> a -> Gen [a]
on iterate(f, x)
script
property v : missing value
property g : mReturn(f)'s |λ|
on |λ|()
if missing value is v then
set v to x
else
set v to g(v)
end if
return v
end |λ|
end script
end iterate

-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
-- The list obtained by applying f
-- to each element of xs.
tell mReturn(f)
set lng to length of xs
set lst to {}
repeat with i from 1 to lng
set end of lst to |λ|(item i of xs, i, xs)
end repeat
return lst
end tell
end map

-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
-- 2nd class handler function lifted into 1st class script wrapper.
if script is class of f then
f
else
script
property |λ| : f
end script
end if
end mReturn

-- gen :: [a] -> Gen a
on gen(xs)
script go
property lng : length of xs
property i : 0
on |λ|()
if i ≥ lng then
missing value
else
set i to 1 + i
item i of xs
end if
end |λ|
end script
end gen

-- showList :: [a] -> String
on showList(xs)
"[" & intercalate(", ", my map(my str, xs)) & "]"
end showList

-- showTuple :: (,) -> String
on showTuple(xs)
"(" & intercalate(", ", my map(my str, xs)) & ")"
end showTuple

-- snd :: (a, b) -> b
on snd(tpl)
if class of tpl is record then
|2| of tpl
else
item 2 of tpl
end if
end snd

-- str :: a -> String
on str(x)
x as string
end str

-- take :: Int -> [a] -> [a]
-- take :: Int -> String -> String
on take(n, xs)
set c to class of xs
if list is c then
if 0 < n then
items 1 thru min(n, length of xs) of xs
else
{}
end if
else if string is c then
if 0 < n then
text 1 thru min(n, length of xs) of xs
else
""
end if
else if script is c then
set ys to {}
repeat with i from 1 to n
set v to |λ|() of xs
if missing value is v then
return ys
else
set end of ys to v
end if
end repeat
return ys
else
missing value
end if
end take

-- unlines :: [String] -> String
on unlines(xs)
-- A single string formed by the intercalation
-- of a list of strings with the newline character.
set {dlm, my text item delimiters} to ¬
{my text item delimiters, linefeed}
set s to xs as text
set my text item delimiters to dlm
s
end unlines
```
Output:
```First 61 terms:
[0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4]

First term of each decimal magnitude:
(Index, Term):
(0, 0)
(37, 11)
(1173, 108)
(35499, 1076)```

## Arturo

Translation of: Nim
```fusc: function [n][
if? or? n=0 n=1 -> n
else [
if? 0=n%2 -> fusc n/2
else -> (fusc (n-1)/2) + fusc (n+1)/2
]
]

print "The first 61 Fusc numbers:"
print map 0..61 => fusc

print "\nThe Fusc numbers whose lengths are greater than those of previous Fusc numbers:"
print "        n   fusc(n)"
print "--------- ---------"
maxLength: 0

loop 0..40000 'i [
f: fusc i
l: size to :string f
if l > maxLength [
maxLength: l
print [
]
]
]
```
Output:
```The first 61 Fusc numbers:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4 9

The Fusc numbers whose lengths are greater than those of previous Fusc numbers:
n   fusc(n)
--------- ---------
0         0
37        11
1173       108
35499      1076```

## AutoHotkey

```fusc:=[], fusc:=0, fusc:=1, n:=1, l:=0, result:=""

while (StrLen(fusc[n]) < 5)
fusc[++n] := Mod(n, 2) ? fusc[floor((n-1)/2)] + fusc[Floor((n+1)/2)] : fusc[floor(n/2)]

while (A_Index <= 61)
result .= (result = "" ? "" : ",") fusc[A_Index-1]

result .= "`n`nfusc number whose length is greater than any previous fusc number length:`nindex`tnumber`n"
for i, v in fusc
if (l < StrLen(v))
l := StrLen(v), result .= i "`t" v "`n"

MsgBox % result
```
Output:
```0,1,1,2,1,3,2,3,1,4,3,5,2,5,3,4,1,5,4,7,3,8,5,7,2,7,5,8,3,7,4,5,1,6,5,9,4,11,7,10,3,11,8,13,5,12,7,9,2,9,7,12,5,13,8,11,3,10,7,11,4
fusc number whose length is greater than any previous fusc number length:
index	number
0	0
37	11
1173	108
35499	1076
699051	10946```

## AWK

```# syntax: GAWK -f FUSC_SEQUENCE.AWK
# converted from C
BEGIN {
for (i=0; i<61; i++) {
printf("%d ",fusc(i))
}
printf("\n")
print("fusc numbers whose length is greater than any previous fusc number length")
printf("%9s %9s\n","fusc","index")
for (i=0; i<=700000; i++) {
f = fusc(i)
leng = num_leng(f)
if (leng > max_leng) {
max_leng = leng
printf("%9s %9s\n",commatize(f),commatize(i))
}
}
exit(0)
}
function commatize(x,  num) {
if (x < 0) {
return "-" commatize(-x)
}
x = int(x)
num = sprintf("%d.",x)
while (num ~ /^[0-9][0-9][0-9][0-9]/) {
sub(/[0-9][0-9][0-9][,.]/,",&",num)
}
sub(/\.\$/,"",num)
return(num)
}
function fusc(n) {
if (n == 0 || n == 1) {
return(n)
}
else if (n % 2 == 0) {
return fusc(n/2)
}
else {
return fusc((n-1)/2) + fusc((n+1)/2)
}
}
function num_leng(n,  sum) {
sum = 1
while (n > 9) {
n = int(n/10)
sum++
}
return(sum)
}
```
Output:
```0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
fusc numbers whose length is greater than any previous fusc number length
fusc     index
0         0
11        37
108     1,173
1,076    35,499
10,946   699,051
```

## BASIC256

```global f, max
max = 36000
dim f(max)

call fusc()

for i = 0 to 60
print f[i]; " ";
next i

print : print
print "     Index         Value"
d = 0
for i = 0 to max-1
if f[i] >= d then
print rjust(string(i),10," "), rjust(string(f[i]),10," ")
if d = 0 then d = 1
d *= 10
end if
next i
end

subroutine fusc()
f = 0 : f = 1
for n = 2 to max-1
if (n mod 2) then
f[n] = f[(n-1)/2] + f[(n+1)/2]
else
f[n] = f[n/2]
end if
next n
end subroutine```

## BQN

Works in: CBQN

`Fusc` computes fusc numbers iteratively.

```Fusc ← {
{
𝕩∾+´(⍷(⌈∾⌊)2÷˜≠𝕩)⊑¨<𝕩
}⍟(𝕩-2)↕2
}

•Show Fusc 61

•Show >⟨"Index"‿"Number"⟩∾{((1+↕4)⊐˜(⌊1+10⋆⁼1⌈|)¨𝕩){𝕨∾𝕨⊑𝕩}¨<𝕩} Fusc 99999```
```⟨ 0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4 ⟩
┌─
╵ "Index" "Number"
0       0
37      11
1173    108
35499   1076
┘```

## C

```#include<limits.h>
#include<stdio.h>

int fusc(int n){
if(n==0||n==1)
return n;
else if(n%2==0)
return fusc(n/2);
else
return fusc((n-1)/2) + fusc((n+1)/2);
}

int numLen(int n){
int sum = 1;

while(n>9){
n = n/10;
sum++;
}

return sum;
}

void printLargeFuscs(int limit){
int i,f,len,maxLen = 1;

printf("\n\nPrinting all largest Fusc numbers upto %d \nIndex-------Value",limit);

for(i=0;i<=limit;i++){
f = fusc(i);
len = numLen(f);

if(len>maxLen){
maxLen = len;
printf("\n%5d%12d",i,f);
}
}
}

int main()
{
int i;

printf("Index-------Value");
for(i=0;i<61;i++)
printf("\n%5d%12d",i,fusc(i));
printLargeFuscs(INT_MAX);
return 0;
}
```

Prints first 61 Fusc numbers followed by the largest numbers :

```Index-------Value
0           0
1           1
2           1
3           2
4           1
5           3
6           2
7           3
8           1
9           4
10           3
11           5
12           2
13           5
14           3
15           4
16           1
17           5
18           4
19           7
20           3
21           8
22           5
23           7
24           2
25           7
26           5
27           8
28           3
29           7
30           4
31           5
32           1
33           6
34           5
35           9
36           4
37          11
38           7
39          10
40           3
41          11
42           8
43          13
44           5
45          12
46           7
47           9
48           2
49           9
50           7
51          12
52           5
53          13
54           8
55          11
56           3
57          10
58           7
59          11
60           4

Printing all largest Fusc numbers upto 2147483647
Index-------Value
37          11
1173         108
35499        1076
699051      10946
103682   19573419
1010747  615164587
```

## C#

```using System;
using System.Collections.Generic;

static class program
{
static int n = 61;
static List<int> l = new List<int>() { 0, 1 };

static int fusc(int n)
{
if (n < l.Count) return l[n];
int f = (n & 1) == 0 ? l[n >> 1] : l[(n - 1) >> 1] + l[(n + 1) >> 1];
}

static void Main(string[] args)
{
bool lst = true; int w = -1, c = 0, t;
string fs = "{0,11:n0}  {1,-9:n0}", res = "";
Console.WriteLine("First {0} numbers in the fusc sequence:", n);
for (int i = 0; i < int.MaxValue; i++)
{
int f = fusc(i); if (lst)
{
if (i < 61) Console.Write("{0} ", f);
else
{
lst = false;
Console.WriteLine();
Console.WriteLine("Points in the sequence where an item has more digits than any previous items:");
Console.WriteLine(fs, "Index\\", "/Value"); Console.WriteLine(res); res = "";
}
}
if ((t = f.ToString().Length) > w)
{
w = t; res += (res == "" ? "" : "\n") + string.Format(fs, i, f);
if (!lst) { Console.WriteLine(res); res = ""; } if (++c > 5) break;
}
}
l.Clear();
}
}
```
Output:
```First 61 numbers in the fusc sequence:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
Points in the sequence where an item has more digits than any previous items:
Index\  /Value
0  0
37  11
1,173  108
35,499  1,076
699,051  10,946
19,573,419  103,682 ```

## C++

Translation of: C#
```#include <iomanip>
#include <iostream>
#include <limits>
#include <sstream>
#include <vector>

const int n = 61;
std::vector<int> l{ 0, 1 };

int fusc(int n) {
if (n < l.size()) return l[n];
int f = (n & 1) == 0 ? l[n >> 1] : l[(n - 1) >> 1] + l[(n + 1) >> 1];
l.push_back(f);
return f;
}

int main() {
bool lst = true;
int w = -1;
int c = 0;
int t;
std::string res;
std::cout << "First " << n << " numbers in the fusc sequence:\n";
for (int i = 0; i < INT32_MAX; i++) {
int f = fusc(i);
if (lst) {
if (i < 61) {
std::cout << f << ' ';
} else {
lst = false;
std::cout << "\nPoints in the sequence where an item has more digits than any previous items:\n";
std::cout << std::setw(11) << "Index\\" << "  " << std::left << std::setw(9) << "/Value\n";
std::cout << res << '\n';
res = "";
}
}
std::stringstream ss;
ss << f;
t = ss.str().length();
ss.str("");
ss.clear();
if (t > w) {
w = t;
res += (res == "" ? "" : "\n");
ss << std::setw(11) << i << "  " << std::left << std::setw(9) << f;
res += ss.str();
if (!lst) {
std::cout << res << '\n';
res = "";
}
if (++c > 5) {
break;
}
}
}
return 0;
}
```
Output:
```First 61 numbers in the fusc sequence:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
Points in the sequence where an item has more digits than any previous items:
Index\  /Value
0  0
37  11
1173  108
35499  1076
699051  10946
19573419  103682```

## CLU

Translation of: Python
```fusc = iter () yields (int)
q: array[int] := array[int]\$
yield(0)
yield(1)

while true do
x: int := array[int]\$reml(q)
yield(x)

x := x + array[int]\$bottom(q)
yield(x)
end
end fusc

longest_fusc = iter () yields (int,int)
sofar: int := 0
count: int := 0

for f: int in fusc() do
if f >= sofar then
yield (count,f)
sofar := 10*sofar
if sofar=0 then sofar:=10 end
end
count := count + 1
end
end longest_fusc

start_up = proc ()
po: stream := stream\$primary_output()

stream\$putl(po, "First 61:")
n: int := 0
for f: int in fusc() do
stream\$puts(po, int\$unparse(f) || " ")
n := n + 1
if n = 61 then break end
end

stream\$putl(po, "\nLength records:")
n := 0
for i, f: int in longest_fusc() do
stream\$putl(po, "fusc(" || int\$unparse(i) || ") = " || int\$unparse(f))
n := n + 1
if n = 5 then break end
end
end start_up```
Output:
```First 61:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
Length records:
fusc(0) = 0
fusc(37) = 11
fusc(1173) = 108
fusc(35499) = 1076
fusc(699051) = 10946```

## D

### Built-in memoization

```import std.functional, std.stdio, std.format, std.conv;

ulong fusc(ulong n) =>
memoize!fuscImp(n);

ulong fuscImp(ulong n) =>
( n < 2 ) ? n :
( n % 2 == 0 ) ? memoize!fuscImp( n/2 ) :
memoize!fuscImp( (n-1)/2 ) + memoize!fuscImp( (n+1)/2 );

void main() {
const N_FIRST=61;
const MAX_N_DIGITS=5;

format!"First %d fusc numbers: "(N_FIRST).write;
foreach( n; 0..N_FIRST ) n.fusc.format!"%d ".write;
writeln;

format!"\nFusc numbers with more digits than any previous (1 to %d digits):"(MAX_N_DIGITS).writeln;
for(auto n=0, ndigits=0; ndigits<MAX_N_DIGITS; n++)
if( n.fusc.to!string.length > ndigits ){
format!"fusc(%d)=%d"( n, n.fusc ).writeln;
ndigits = n.fusc.to!string.length.to!int;
}
}
```
Output:
```First 61 fusc numbers: 0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

Fusc numbers with more digits than any previous (1 to 5 digits):
fusc(0)=0
fusc(37)=11
fusc(1173)=108
fusc(35499)=1076
fusc(699051)=10946```

### Manual memoization

```import std.stdio, std.format, std.conv;

int[] fusc_cache = [0, 1];
int fusc(int n) {
// Ensure cache contains all missing numbers until n
for(auto i=fusc_cache.length;i<=n;i++)
fusc_cache ~= i%2 == 0
? fusc_cache[i/2]
: fusc_cache[(i-1)/2] + fusc_cache[(i + 1)/2];
// Solve using cache
return fusc_cache[n];
}

void main() {
const N_FIRST=61;
const MAX_N_DIGITS=6;

format!"First %d fusc numbers: "(N_FIRST).write;
foreach( n; 0..N_FIRST ) n.fusc.format!"%d ".write;
writeln;

format!"\nFusc numbers with more digits than any previous (1 to %d digits):"(MAX_N_DIGITS).writeln;
for(auto n=0, ndigits=0; ndigits<MAX_N_DIGITS; n++)
if( n.fusc.to!string.length > ndigits ){
format!"fusc(%d)=%d"( n, n.fusc ).writeln;
ndigits = n.fusc.to!string.length.to!int;
}
}
```
Output:
```First 61 fusc numbers: 0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

Fusc numbers with more digits than any previous (1 to 6 digits):
fusc(0)=0
fusc(37)=11
fusc(1173)=108
fusc(35499)=1076
fusc(699051)=10946
fusc(19573419)=103682```

See Pascal.

## Dyalect

Translation of: C#
```let n = 61
let l = [0, 1]

func fusc(n) {
return l[n] when n < l.Length()
let f = (n &&& 1) == 0 ? l[n >>> 1] : l[(n - 1) >>> 1] + l[(n + 1) >>> 1]
return f
}

var lst = true
var w = -1
var c = 0
var t = nil
var res = ""

print("First \(n) numbers in the fusc sequence:")
for i in 0..Integer.Max {
let f = fusc(i)
if lst {
if i < 61 {
print("\(f) ", terminator: "")
} else {
lst = false
print("")
print("Points in the sequence where an item has more digits than any previous items:")
print("Index/Value:")
print(res)
res = ""
}
}
t = f.ToString().Length()
if t > w {
w = t
res += (res == "" ? "" : "\n") + "\(i)/\(f)"
if !lst {
print(res)
res = ""
}
c += 1
if c > 5 {
break
}
}
}
l.Clear()```
Output:
```First 61 numbers in the fusc sequence:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
Points in the sequence where an item has more digits than any previous items:
Index/Value:
0/0
37/11
1173/108
35499/1076
699051/10946
19573419/103682```

## F#

### The Function

```// Generate the fusc sequence. Nigel Galloway: March 20th., 2019
let fG n=seq{for (n,g) in Seq.append n  |> Seq.pairwise do yield n; yield n+g}
let fusc=seq{yield 0; yield! Seq.unfold(fun n->Some(n,fG n))(seq)|>Seq.concat}|> Seq.mapi(fun n g->(n,g))
```

Print first 62 elements
```fusc |> Seq.take 61 |> Seq.iter(fun(_,g)->printf "%d " g); printfn ""
```
Output:
```0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
```
Show the fusc number (and its index) whose length is greater than any previous fusc number length

The first 6 take only 10 secs so let me be more ambitious

```let fN=let mutable n=0 in (fun (_,g)->if g>=n then n<-pown 10 (string g).Length; true else false)
fusc |> Seq.filter fN |> Seq.take 7 |> Seq.iter(fun(n,g)->printfn "fusc %d -> %d" n g)
```
Output:
```fusc 0 -> 0
fusc 37 -> 11
fusc 1173 -> 108
fusc 35499 -> 1076
fusc 699051 -> 10946
fusc 19573419 -> 103682
fusc 615164587 -> 1010747
Real: 00:06:03.801, CPU: 00:06:03.140, GC gen0: 21336, gen1: 0
```

## Factor

```USING: arrays assocs formatting io kernel make math math.parser
math.ranges namespaces prettyprint sequences
tools.memory.private ;
IN: rosetta-code.fusc

<PRIVATE

: (fusc) ( n -- seq )
[ 2 ] dip [a,b) [
0 , 1 , [
[ building get ] dip dup even?
[ 2/ swap nth ]
[ [ 1 - 2/ ] [ 1 + 2/ ] 2bi [ swap nth ] 2bi@ + ]
if ,
] each
] { } make ;

: increases ( seq -- assoc )
[ 0 ] dip [
[
2array 2dup first number>string length <
[ [ 1 + ] [ , ] bi* ] [ drop ] if
] each-index
] { } make nip ;

PRIVATE>

: fusc ( n -- seq )
dup 3 < [ { 0 1 } swap head ] [ (fusc) ] if ;

: fusc-demo ( -- )
"First 61 fusc numbers:" print 61 fusc [ pprint bl ] each
nl nl
"Fusc numbers with more digits than all previous ones:"
print "Value   Index\n======  =======" print
1,000,000 fusc increases
[ [ commas ] bi@ "%-6s  %-7s\n" printf ] assoc-each ;

MAIN: fusc-demo
```
Output:
```First 61 fusc numbers:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

Fusc numbers with more digits than all previous ones:
Value   Index
======  =======
0       0
11      37
108     1,173
1,076   35,499
10,946  699,051
```

## Forth

```\ Gforth 0.7.9_20211014

: fusc ( n -- n)                     \  input n -- output fusc(n)
dup  dup  0= swap  1 = or          \  n = 0 or 1
if  exit                           \  return n
else dup 2 mod 0=                  \  test even
if 2/ recurse                 \  even fusc(n)= fusc(n/2)
else dup  1- 2/ recurse       \  odd  fusc(n) = fusc((n-1)/2) +
swap 1+ 2/ recurse  +    \                 fusc((n+1)/2)
then
then
;

: cntDigits ( n -- n )               \ returns the numbers of digits
0 begin 1+ swap
10 /
swap  over
0= until
swap drop
;

: fuscLen ( n -- )                    \ count until end index
cr 1   swap  0
do
i fusc cntDigits
over > if 1+
." fusc( " i . ." ) : "
i fusc  . cr
then
loop
;

: firstFusc ( n -- )                  \ show  fusc(i)   until  limit
dup ." First " . ." fusc(n) : " cr
0 do  I fusc .  loop cr
;

61 firstFusc

20 1000 1000 * * fuscLen

bye
```
Output:
```First 61 fusc(n) :
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

fusc( 37 ) : 11
fusc( 1173 ) : 108
fusc( 35499 ) : 1076
fusc( 699051 ) : 10946
fusc( 19573419 ) : 103682
```

## FreeBASIC

```' version 01-03-2019
' compile with: fbc -s console

#Define max 20000000

Dim Shared As UInteger f(max)

Sub fusc

f(0) = 0
f(1) = 1

For n As UInteger = 2 To max
If n And 1 Then
f(n) = f((n -1) \ 2) + f((n +1) \ 2)
Else
f(n) = f(n \ 2)
End If
Next

End Sub

' ------=< MAIN >=------

Dim As UInteger i, d
Dim As String fs

fusc

For i = 0 To 60
Print f(i); " ";
Next

Print : Print
Print "       Index       Value"
For i = 0 To max
If f(i) >= d Then
Print Using "###########," ; i; f(i)
If d = 0 Then d = 1
d *= 10
End If
Next

' empty keyboard buffer
While Inkey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End
```
Output:
```0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

Index       Value
0           0
37          11
1,173         108
35,499       1,076
699,051      10,946
19,573,419     103,682```

## Fōrmulæ

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for storage and transfer purposes more than visualization and edition.

Programs in Fōrmulæ are created/edited online in its website, However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.

## Go

```package main

import (
"fmt"
"strconv"
)

func fusc(n int) []int {
if n <= 0 {
return []int{}
}
if n == 1 {
return []int{0}
}
res := make([]int, n)
res = 0
res = 1
for i := 2; i < n; i++ {
if i%2 == 0 {
res[i] = res[i/2]
} else {
res[i] = res[(i-1)/2] + res[(i+1)/2]
}
}
return res
}

func fuscMaxLen(n int) []int {
maxLen := -1
maxFusc := -1
f := fusc(n)
var res []int
for i := 0; i < n; i++ {
if f[i] <= maxFusc {
continue // avoid expensive strconv operation where possible
}
maxFusc = f[i]
le := len(strconv.Itoa(f[i]))
if le > maxLen {
res = append(res, int{i, f[i]})
maxLen = le
}
}
return res
}

func commatize(n int) string {
s := fmt.Sprintf("%d", n)
if n < 0 {
s = s[1:]
}
le := len(s)
for i := le - 3; i >= 1; i -= 3 {
s = s[0:i] + "," + s[i:]
}
if n >= 0 {
return s
}
return "-" + s
}

func main() {
fmt.Println("The first 61 fusc numbers are:")
fmt.Println(fusc(61))
fmt.Println("\nThe fusc numbers whose length > any previous fusc number length are:")
res := fuscMaxLen(20000000)  // examine first twenty million numbers say
for i := 0; i < len(res); i++ {
fmt.Printf("%7s (index %10s)\n", commatize(res[i]), commatize(res[i]))
}
}
```
Output:
```The first 61 fusc numbers are:
[0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4]

The fusc numbers whose length > any previous fusc number length are:
0 (index          0)
11 (index         37)
108 (index      1,173)
1,076 (index     35,499)
10,946 (index    699,051)
103,682 (index 19,573,419)
```

## Groovy

Translation of: Java
```class FuscSequence {
static void main(String[] args) {
println("Show the first 61 fusc numbers (starting at zero) in a horizontal format")
for (int n = 0; n < 61; n++) {
printf("%,d ", fusc[n])
}

println()
println()
println("Show the fusc number (and its index) whose length is greater than any previous fusc number length.")
int start = 0
for (int i = 0; i <= 5; i++) {
int val = i != 0 ? (int) Math.pow(10, i) : -1
for (int j = start; j < FUSC_MAX; j++) {
if (fusc[j] > val) {
printf("fusc[%,d] = %,d%n", j, fusc[j])
start = j
break
}
}
}
}

private static final int FUSC_MAX = 30000000
private static int[] fusc = new int[FUSC_MAX]

static {
fusc = 0
fusc = 1
for (int n = 2; n < FUSC_MAX; n++) {
int n2 = (int) (n / 2)
int n2m = (int) ((n - 1) / 2)
int n2p = (int) ((n + 1) / 2)
fusc[n] = n % 2 == 0
? fusc[n2]
: fusc[n2m] + fusc[n2p]
}
}
}
```
Output:
```Show the first 61 fusc numbers (starting at zero) in a horizontal format
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

Show the fusc number (and its index) whose length is greater than any previous fusc number length.
fusc = 0
fusc = 11
fusc[1,173] = 108
fusc[35,499] = 1,076
fusc[699,051] = 10,946
fusc[19,573,419] = 103,682```

```---------------------- FUSC SEQUENCE ---------------------

fusc :: Int -> Int
fusc i
| 1 > i = 0
| otherwise = fst \$ go (pred i)
where
go n
| 0 == n = (1, 0)
| even n = (x + y, y)
| otherwise = (x, x + y)
where
(x, y) = go (div n 2)

--------------------------- TEST -------------------------
main :: IO ()
main = do
putStrLn "First 61 terms:"
print \$ fusc <\$> [0 .. 60]
putStrLn "\n(Index, Value):"
mapM_ print \$ take 5 widths

widths :: [(Int, Int)]
widths =
fmap
(\(_, i, x) -> (i, x))
(iterate nxtWidth (2, 0, 0))

nxtWidth :: (Int, Int, Int) -> (Int, Int, Int)
nxtWidth (w, i, v) = (succ w, j, x)
where
fi = (,) <*> fusc
(j, x) =
until
((w <=) . length . show . snd)
(fi . succ . fst)
(fi i)
```
Output:
```First 61 terms:
[0,1,1,2,1,3,2,3,1,4,3,5,2,5,3,4,1,5,4,7,3,8,5,7,2,7,5,8,3,7,4,5,1,6,5,9,4,11,7,10,3,11,8,13,5,12,7,9,2,9,7,12,5,13,8,11,3,10,7,11,4]

(Index, Value):
(0,0)
(37,11)
(1173,108)
(35499,1076)
(699051,10946)```

Another version using infinite list:

```zipWithLazy :: (a -> b -> c) -> [a] -> [b] -> [c]
zipWithLazy f ~(x : xs) ~(y : ys) =
f x y : zipWithLazy f xs ys

fuscs :: [Integer]
fuscs = 0 : s
where
s = 1 : concat (zipWithLazy f s (tail s))
f x y = [x, x + y]

widths :: [(Int, Integer)]
widths = map head \$ scanl f (zip [0 ..] fuscs) [2 ..]
where
f fis w = dropWhile ((< w) . length . show . snd) fis

main :: IO ()
main = do
putStrLn "First 61 terms:"
print \$ take 61 fuscs
putStrLn "\n(Index, Value):"
mapM_ print \$ take 5 widths
```
Output:
```First 61 terms:
[0,1,1,2,1,3,2,3,1,4,3,5,2,5,3,4,1,5,4,7,3,8,5,7,2,7,5,8,3,7,4,5,1,6,5,9,4,11,7,10,3,11,8,13,5,12,7,9,2,9,7,12,5,13,8,11,3,10,7,11,4]

(Index, Value):
(0,0)
(37,11)
(1173,108)
(35499,1076)
(699051,10946)
```

## J

```fusc_term =: ({~ -:@#)`([: +/ ({~ ([: -: _1 1 + #)))@.(2 | #)
fusc =: (, fusc_term)@:]^:[ 0 1"_

NB. show the first 61 fusc numbers (starting at zero) in a horizontal format.
61 {. fusc 70
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

9!:17]2 2 NB. specify bottom right position in box

FUSC =: fusc 99999
DIGITS =: ; ([: # 10&#.inv)&.> FUSC

(;: 'index value') ,. <"0(,: {&A) DIGITS i. 1 2 3 4
┌─────┬─┬──┬────┬─────┐
│index│0│37│1173│35499│
├─────┼─┼──┼────┼─────┤
│value│0│11│ 108│ 1076│
└─────┴─┴──┴────┴─────┘
```

## Java

```public class FuscSequence {

public static void main(String[] args) {
System.out.println("Show the first 61 fusc numbers (starting at zero) in a horizontal format");
for ( int n = 0 ; n < 61 ; n++ ) {
System.out.printf("%,d ", fusc[n]);
}

System.out.printf("%n%nShow the fusc number (and its index) whose length is greater than any previous fusc number length.%n");
int start = 0;
for (int i = 0 ; i <= 5 ; i++ ) {
int val = i != 0 ? (int) Math.pow(10, i) : -1;
for ( int j = start ; j < FUSC_MAX ; j++ ) {
if ( fusc[j] > val ) {
System.out.printf("fusc[%,d] = %,d%n", j, fusc[j] );
start = j;
break;
}
}
}
}

private static final int FUSC_MAX = 30000000;
private static int[] fusc = new int[FUSC_MAX];

static {
fusc = 0;
fusc = 1;
for ( int n = 2 ; n < FUSC_MAX ; n++ ) {
fusc[n] = (n % 2 == 0 ? fusc[n/2] : fusc[(n-1)/2] + fusc[(n+1)/2]);
}
}
}
```
Output:
```Show the first 61 fusc numbers (starting at zero) in a horizontal format
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

Show the fusc number (and its index) whose length is greater than any previous fusc number length.
fusc = 0
fusc = 11
fusc[1,173] = 108
fusc[35,499] = 1,076
fusc[699,051] = 10,946
fusc[19,573,419] = 103,682
```

## JavaScript

### Functional

Translation of: Python

A composition of pure generic functions:

```(() => {
"use strict";

// ---------------------- FUSC -----------------------

// fusc :: Int -> Int
const fusc = i => {
const go = n =>
0 === n ? [
1, 0
] : (() => {
const [x, y] = go(Math.floor(n / 2));

return 0 === n % 2 ? (
[x + y, y]
) : [x, x + y];
})();

return 1 > i ? (
0
) : go(i - 1);
};

// ---------------------- TEST -----------------------
const main = () => {
const terms = enumFromTo(0)(60).map(fusc);

return [
"First 61 terms:",
`[\${terms.join(",")}]`,
"",
"(Index, Value):",
firstWidths(5).reduce(
(a, x) => [x.slice(1), ...a],
[]
)
.map(([i, x]) => `(\${i}, \${x})`)
.join("\n")
]
.join("\n");
};

// firstWidths :: Int -> [(Int, Int)]
const firstWidths = n => {
const nxtWidth = xs => {
const
fi = fanArrow(fusc)(x => x),
[w, i] = xs,
[x, j] = Array.from(
until(
v => w <= `\${v}`.length
)(
v => fi(1 + v)
)(fi(i))
);

return [
[1 + w, j, x],
...xs
];
};

return until(x => n < x)(
nxtWidth
)([
[2, 0, 0]
]);
};

// ---------------- GENERIC FUNCTIONS ----------------

// enumFromTo :: Int -> Int -> [Int]
const enumFromTo = m =>
n => Array.from({
length: 1 + n - m
}, (_, i) => m + i);

// fanArrow (&&&) ::
// (a -> b) -> (a -> c) -> (a -> (b, c))
const fanArrow = f =>
// A combined function, given f and g,
// from x to a tuple of (f(x), g(x))
// ((,) . f <*> g)
g => x => [f(x), g(x)];

// until :: (a -> Bool) -> (a -> a) -> a -> a
const until = p =>
// The value resulting from successive applications
// of f to f(x), starting with a seed value x,
// and terminating when the result returns true
// for the predicate p.
f => {
const go = x =>
p(x) ? x : go(f(x));

return go;
};

// MAIN ---
return main();
})();
```
Output:
```First 61 terms:
[0,1,1,2,1,3,2,3,1,4,3,5,2,5,3,4,1,5,4,7,3,8,5,7,2,7,5,8,3,7,4,5,1,6,5,9,4,11,7,10,3,11,8,13,5,12,7,9,2,9,7,12,5,13,8,11,3,10,7,11,4]

(Index, Value):
(0, 0)
(37, 11)
(1173, 108)
(35499, 1076)
(699051, 10946)```

## jq

Works with: jq

Works with gojq, the Go implementation of jq

Preliminaries

```# input should be a non-negative integer
def commatize:
# "," is 44
def digits: tostring | explode | reverse;
[foreach digits[] as \$d (-1; .+1;
(select(. > 0 and . % 3 == 0)|44), \$d)]
| reverse | implode  ;

def lpad(\$len): tostring | (\$len - length) as \$l | (" " * \$l)[:\$l] + .;```

Fusc Sequence

```# Save space by truncating the beginning of the array
def fusc:
0, 1,
foreach range(2; infinite) as \$n ([0, 1];
(\$n % 2 == 0) as \$even
| if \$even then . + [.] else.[1:] + [. + .] end;
.[-1] );

# Report first longest
def fusc( \$mx ):

foreach limit( \$mx; fusc ) as \$f ({ maxLen: 0, n: 0 };
.emit = false
| ("\(\$f)"|length) as \$len
| if \$len > .maxLen
then .maxLen = \$len
| .emit = "\(.n|l)  \(\$f|commatize)"
else .
end
| .n += 1
;
select(.emit).emit
);

# First \$first numbers in the fusc sequence
61 as \$first
| 2e6 as \$mx
| "The first \(\$first) numbers in the fusc sequence are:",
([limit(\$first; fusc)]| map(tostring) | join(" ")) ,

"\nFirst terms longer than any previous ones for indices < \(\$mx + 0 |commatize):",
"     Index  Value",
fusc(\$mx)```
Output:
```The first 61 numbers in the fusc sequence are:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

First terms longer than any previous ones for indices < 20,000,000:
Index  Value
0  0
37  11
1,173  108
35,499  1,076
699,051  10,946
19,573,419  103,682

```

## Julia

```using Memoize, Formatting

@memoize function sternbrocot(n)
if n < 2
return n
elseif iseven(n)
return sternbrocot(div(n, 2))
else
m = div(n - 1, 2)
return sternbrocot(m) + sternbrocot(m + 1)
end
end

function fusclengths(N=100000000)
println("sequence number : fusc value")
maxlen = 0
for i in 0:N
x = sternbrocot(i)
if (len = length(string(x))) > maxlen
println(lpad(format(i, commas=true), 15), " : ", format(x, commas=true))
maxlen = len
end
end
end

println("The first 61 fusc numbers are: ", [sternbrocot(x) for x in 0:60])
fusclengths()
```
Output:
```The first 61 fusc numbers are: [0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6,
5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4]
sequence number : fusc value
0 : 0
37 : 11
1,173 : 108
35,499 : 1,076
699,051 : 10,946
19,573,419 : 103,682
```

## Kotlin

Translation of: Go
```// Version 1.3.21

fun fusc(n: Int): IntArray {
if (n <= 0) return intArrayOf()
if (n == 1) return intArrayOf(0)
val res = IntArray(n)
res = 1
for (i in 2 until n) {
if (i % 2 == 0) {
res[i] = res[i / 2]
} else {
res[i] = res[(i - 1) / 2] + res[(i + 1) / 2]
}
}
return res
}

fun fuscMaxLen(n: Int): List<Pair<Int, Int>> {
var maxLen = -1
var maxFusc = -1
val f = fusc(n)
val res = mutableListOf<Pair<Int, Int>>()
for (i in 0 until n) {
if (f[i] <= maxFusc) continue // avoid string conversion
maxFusc = f[i]
val len = f[i].toString().length
if (len > maxLen) {
maxLen = len
}
}
return res
}

fun main() {
println("The first 61 fusc numbers are:")
println(fusc(61).asList())
println("\nThe fusc numbers whose length > any previous fusc number length are:")
val res = fuscMaxLen(20_000_000)  // examine first 20 million numbers say
for (r in res) {
System.out.printf("%,7d (index %,10d)\n", r.second, r.first)
}
}
```
Output:
```The first 61 fusc numbers are:
[0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4]

The fusc numbers whose length > any previous fusc number length are:
0 (index          0)
11 (index         37)
108 (index      1,173)
1,076 (index     35,499)
10,946 (index    699,051)
103,682 (index 19,573,419)
```

## Lua

Translation of: C
```function fusc(n)
n = math.floor(n)
if n == 0 or n == 1 then
return n
elseif n % 2 == 0 then
return fusc(n / 2)
else
return fusc((n - 1) / 2) + fusc((n + 1) / 2)
end
end

function numLen(n)
local sum = 1
while n > 9 do
n = math.floor(n / 10)
sum = sum + 1
end
return sum
end

function printLargeFuscs(limit)
print("Printing all largest Fusc numbers up to " .. limit)
print("Index-------Value")
local maxLen = 1
for i=0,limit do
local f = fusc(i)
local le = numLen(f)
if le > maxLen then
maxLen = le
print(string.format("%5d%12d", i, f))
end
end
end

function main()
print("Index-------Value")
for i=0,60 do
print(string.format("%5d%12d", i, fusc(i)))
end
printLargeFuscs(math.pow(2, 31) - 1)
end

main()
```
Output:
```Index-------Value
0           0
1           1
2           1
3           2
4           1
5           3
6           2
7           3
8           1
9           4
10           3
11           5
12           2
13           5
14           3
15           4
16           1
17           5
18           4
19           7
20           3
21           8
22           5
23           7
24           2
25           7
26           5
27           8
28           3
29           7
30           4
31           5
32           1
33           6
34           5
35           9
36           4
37          11
38           7
39          10
40           3
41          11
42           8
43          13
44           5
45          12
46           7
47           9
48           2
49           9
50           7
51          12
52           5
53          13
54           8
55          11
56           3
57          10
58           7
59          11
60           4
Printing all largest Fusc numbers up to 2147483647
Index-------Value
37          11
1173         108
35499        1076
699051       10946```

## Mathematica / Wolfram Language

```ClearAll[Fusc]
Fusc := 0
Fusc := 1
Fusc[n_] := Fusc[n] = If[EvenQ[n], Fusc[n/2], Fusc[(n - 1)/2] + Fusc[(n + 1)/2]]
Fusc /@ Range[0, 60]
res = {{0, 1}};
i = 0;
PrintTemporary[Dynamic[{res, i}]];
While[Length[res] < 6,
f = Fusc[i];
If[IntegerLength[res[[-1, -1]]] < IntegerLength[f],
AppendTo[res, {i, f}]
];
i++;
];
res
```
Output:
```{0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4}
{{0, 1}, {37, 11}, {1173, 108}, {35499, 1076}, {699051, 10946}, {19573419, 103682}}```

## Nim

### Using recursive procedure

This is the simplest way to compute the sequence, but not very efficient here as we compute several times the same values. The algorithm could be improved by using a cache to keep the values.

```import strformat

func fusc(n: int): int =
if n == 0 or n == 1:
n
elif n mod 2 == 0:
fusc(n div 2)
else:
fusc((n - 1) div 2) + fusc((n + 1) div 2)

echo "The first 61 Fusc numbers:"
for i in 0..61:
write(stdout, fmt"{fusc(i)} ")
echo "\n\nThe Fusc numbers whose lengths are greater than those of previous Fusc numbers:"
echo fmt"        n   fusc(n)"
echo    "--------- ---------"
var maxLength = 0
for i in 0..700_000:
var f = fusc(i)
var length = len(\$f)
if length > maxLength:
maxLength = length
echo fmt"{i:9} {f:9}"
```
Output:
```The first 61 Fusc numbers:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4 9

The Fusc numbers whose lengths are greater than those of previous Fusc numbers:
n   fusc(n)
--------- ---------
0         0
37        11
1173       108
35499      1076
699051     10946
```

### Using iterators and double queues (deques)

Translation of: Python

This is a translation of the Python procedural algorithm, using iterators instead of generators. It allows to compute the seven first Fusc numbers whose lengths are greater than those of previous Fusc numbers.

```import deques, strformat

iterator fusc(): int =
var q = .toDeque()
yield 0
yield 1

while true:
var val = q.popFirst()
yield val

val += q
yield val

iterator longestFusc(): tuple[idx, val: int] =
var sofar = 0
var i = -1
for f in fusc():
inc i
if f >= sofar:
yield (i, f)
sofar = if sofar == 0: 10 else: 10 * sofar

#———————————————————————————————————————————————————————————————————————————————————————————————————

const
MaxFusc = 61
LongestCount = 7

echo &"First {MaxFusc}:"
var i = -1
for f in fusc():
inc i
stdout.write f
if i == MaxFusc:
echo ""
break
stdout.write ' '

echo "\nLength records:"
var count = 0
for (i, f) in longestFusc():
inc count
echo &"fusc({i}) = {f}"
if count == LongestCount:
break
```
Output:
```First 61:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4 9

Length records:
fusc(0) = 0
fusc(37) = 11
fusc(1173) = 108
fusc(35499) = 1076
fusc(699051) = 10946
fusc(19573419) = 103682
fusc(615164587) = 1010747```

## OCaml

```let seq_fusc =
let rec next x xs () =
match xs () with
| Seq.Nil -> assert false
| Cons (x', xs') -> Seq.Cons (x' + x, Seq.cons x' (next x' xs'))
in
let rec tail () = Seq.Cons (1, next 1 tail) in
Seq.cons 0 (Seq.cons 1 tail)

let seq_first_of_lengths =
let rec next i l sq () =
match sq () with
| Seq.Nil -> Seq.Nil
| Cons (x, xs) when x >= l -> Cons ((i, x), next (succ i) (10 * l) xs)
| Cons (_, xs) -> next (succ i) l xs ()
in next 0 10

let () =
seq_fusc |> Seq.take 61 |> Seq.iter (Printf.printf " %u") |> print_newline
and () =
seq_fusc |> seq_first_of_lengths |> Seq.take 7
|> Seq.iter (fun (i, x) -> Printf.printf "%9u @ %u%!\n" x i)
```

Compiled by ocamlopt the program finishes in about 8 minutes.

Output:
``` 0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
11 @ 37
108 @ 1173
1076 @ 35499
10946 @ 699051
103682 @ 19573419
1010747 @ 615164587
10059505 @ 18611524949
```

With `take 8`, a further line would be output after almost 3 hours:

`102334155 @ 366503875925`

## Pascal

Works with: Free Pascal

Using dynamic array.To speed things up using Pointer. Found the indices of a specific base to oszillating.Tried power of phi with more success 11 ~ phi^5

```program fusc;
uses
sysutils;
const
{\$IFDEF FPC}
MaxIdx = 1253 * 1000 * 1000; //19573420; // must be even
{\$ELSE}
// Dynamics arrays in Delphi cann't be to large
MaxIdx = 19573420;
{\$ENDIF}

type
tFuscElem = LongWord;
tFusc = array of tFuscElem;
var
FuscField : tFusc;

function commatize(n:NativeUint):string;
var
l,i : NativeUint;
begin
str(n,result);
l := length(result);
//no commatize
if l < 4 then
exit;
//new length
i := l+ (l-1) DIV 3;
setlength(result,i);
//copy chars to the right place
While i <> l do
Begin
result[i]:= result[l];result[i-1]:= result[l-1];
result[i-2]:= result[l-2];result[i-3]:= ',';
dec(i,4);dec(l,3);
end;
end;

procedure OutFusc(StartIdx,EndIdx :NativeInt;const FF:tFusc);
Begin
IF StartIdx < Low(FF) then StartIdx :=Low(FF);
IF EndIdx > High(FF) then EndIdx := High(FF);
For StartIdx := StartIdx to EndIdx do
write(FF[StartIdx],' ');
writeln;
end;

procedure FuscCalc(var FF:tFusc);
var
pFFn,pFFi : ^tFuscElem;
i,n,sum : NativeUint;
Begin
FF:= 0;
FF:= 1;
n := 2;
i := 1;
pFFn := @FF[n];
pFFi := @FF[i];
sum := pFFi^;
while n <= MaxIdx-2 do
begin
//even
pFFn^ := sum;//FF[n] := FF[i];
//odd
inc(pFFi);//FF[i+1]
inc(pFFn);//FF[n+1]
sum := sum+pFFi^;
pFFn^:= sum; //FF[n+1] := FF[i]+FF[i+1];
sum := pFFi^;
inc(pFFn);
inc(n,2);
//inc(i);
end;
end;

begin
writeln('Fusc numbers with more digits in base ',base,' than all previous ones:');
writeln('Value':10,'Index':10,'  IndexNum/IndexNumBefore');
writeln('======':10,' =======':14);
end;

procedure CheckFuscDigits(const FF:tFusc;Base:NativeUint);
var
pFF : ^tFuscElem;
Dig,
i,lastIdx: NativeInt;
Begin
Dig := -1;
i := 0;
lastIdx := 0;
pFF := @FF;// aka FF[i]
repeat
//search in tight loop speeds up
repeat
inc(pFF);
inc(i);
until pFF^ >Dig;

if i>= MaxIdx then
BREAK;
//output
write(commatize(pFF^):10,commatize(i):14);//,DIG:10);
IF lastIdx> 0 then
write(i/lastIdx:12:7);
writeln;
lastIdx := i;
IF Dig >0 then
Dig := Dig*Base+Base-1
else
Dig := Base-1;
until false;
writeln;
end;

BEGIN
setlength(FuscField,MaxIdx);
FuscCalc(FuscField);
writeln('First 61 fusc numbers:');
OutFusc(0,60,FuscField);

CheckFuscDigits(FuscField,10);
CheckFuscDigits(FuscField,11); //11 ~phi^5  1.6180..^5 = 11,09
setlength(FuscField,0);
END.
```
Output:
```First 61 fusc numbers:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
Fusc numbers with more digits in base 10 than all previous ones:
Value     Index  IndexNum/IndexNumBefore
======       =======
1             1
11            37  37.0000000
108         1,173  31.7027027
1,076        35,499  30.2634271
10,946       699,051  19.6921322
103,682    19,573,419  27.9999871
1,010,747   615,164,587  31.4285709

Fusc numbers with more digits in base 11 than all previous ones:
Value     Index  IndexNum/IndexNumBefore
======       =======
1             1
11            37  37.0000000
123         1,195  32.2972973
1,364        38,229  31.9907950
15,127     1,223,339  32.0002877
167,761    39,146,837  31.9999910
1,860,498 1,252,698,795  32.0000003

real  0m1,968s  user  0m1,594s  sys 0m0,373s```

## Perl

Borrowing from the Stern-Brocot sequence task.

```use strict;
use warnings;
use feature 'say';

sub comma { reverse ((reverse shift) =~ s/(.{3})/\$1,/gr) =~ s/^,//r }

sub stern_diatomic {
my (\$p,\$q,\$i) = (0,1,shift);
while (\$i) {
if (\$i & 1) { \$p += \$q; } else { \$q += \$p; }
\$i >>= 1;
}
\$p;
}

say "First 61 terms of the Fusc sequence:\n" . join ' ', map { stern_diatomic(\$_) } 0..60;
say "\nIndex and value for first term longer than any previous:";

my \$i =  0;
my \$l = -1;
while (\$l < 5) {
my \$v = stern_diatomic(\$i);
printf("%15s : %s\n", comma(\$i), comma(\$v)) and \$l = length \$v if length \$v > \$l;
\$i++;
}
```
Output:
```First 61 terms of the Fusc sequence:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

Index and value for first term longer than any previous:
0 : 0
37 : 11
1,173 : 108
35,499 : 1,076
699,051 : 10,946```

## Phix

Note that phix is 1-indexed. While there are no commas in the first 61 entries, it felt more in line with the task requirements to forego the standard comma-separated %v output.

```constant limit = 20_000_000
sequence fuscs = repeat(0,limit); -- NB 1-based indexing; fusc(0)===fuscs
fuscs = 1                                        -- ie fusc(1):=1
for n=3 to limit do
fuscs[n] = iff(remainder(n-1,2)?fuscs[n/2]+fuscs[n/2+1]:fuscs[(n+1)/2])
end for
--printf(1,"First 61 terms of the Fusc sequence:\n%v\n",{fuscs[1..61]})
string s = ""
for n=1 to 61 do s&=sprintf("%,d ",fuscs[n]) end for
printf(1,"First 61 terms of the Fusc sequence:\n%s\n\n",{s})
printf(1,"Elements with more digits than any previous items:\n")
printf(1,"          Index : Value\n")
integer d = 0
for n=1 to length(fuscs) do
if fuscs[n]>=d then
printf(1,"%,15d : %,d\n",{n-1,fuscs[n]})
d = iff(d=0?10:d*10)
end if
end for
```
Output:
```First 61 terms of the Fusc sequence:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

Elements with more digits than any previous items:
Index : Value
0 : 0
37 : 11
1,173 : 108
35,499 : 1,076
699,051 : 10,946
19,573,419 : 103,682
```

## Picat

```main =>
println("First 61 fusc numbers:"),
println([fusc(I) : I in 0..60]),
nl,
println("Points in the sequence whose length is greater than any previous fusc number length:\n"),
println("   Index     fusc  Len"),
largest_fusc_string(20_000_000).

table
fusc(0) = 0.
fusc(1) = 1.
fusc(N) = fusc(N//2), even(N) => true.
fusc(N) = fusc((N-1)//2) + fusc((N+1)//2) => true.

largest_fusc_string(Limit) =>
largest_fusc_string(0,Limit,0).

largest_fusc_string(Limit,Limit,_).
largest_fusc_string(N,Limit,LargestLen) :-
N <= Limit,
F = fusc(N),
Len = F.to_string.len,
(Len > LargestLen ->
printf("%8d %8d %4d\n",N,F,Len),
LargestLen1 = Len
;
LargestLen1 = LargestLen
),
largest_fusc_string(N+1,Limit,LargestLen1).```
Output:
```First 61 fusc numbers:
[0,1,1,2,1,3,2,3,1,4,3,5,2,5,3,4,1,5,4,7,3,8,5,7,2,7,5,8,3,7,4,5,1,6,5,9,4,11,7,10,3,11,8,13,5,12,7,9,2,9,7,12,5,13,8,11,3,10,7,11,4]

Points in the sequence whose length is greater than any previous fusc number length:

Index     fusc  Len
0        0    1
37       11    2
1173      108    3
35499     1076    4
699051    10946    5
19573419   103682    6```

## Processing

```void setup() {
println("First 61 terms:");
for (int i = 0; i < 60; i++) {
print(fusc(i) + " ");
}
println(fusc(60));
println();
println("Sequence elements where number of digits of the value increase:");
int max_len = 0;
for (int i = 0; i < 700000; i++) {
int temp = fusc(i);
if (str(temp).length() > max_len) {
max_len = str(temp).length();
println("(" + i + ", " + temp + ")");
}
}
}

int fusc(int n) {
if (n <= 1) {
return n;
} else if (n % 2 == 0) {
return fusc(n / 2);
} else {
return fusc((n - 1) / 2) + fusc((n + 1) / 2);
}
}```
Output:
```First 61 terms:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

Sequence elements where number of digits of the value increase:
(0, 0)
(37, 11)
(1173, 108)
(35499, 1076)
(699051, 10946)```

## Prolog

Works with: SWI Prolog
```:- dynamic fusc_cache/2.

fusc(0, 0):-!.
fusc(1, 1):-!.
fusc(N, F):-
fusc_cache(N, F),
!.
fusc(N, F):-
0 is N mod 2,
!,
M is N//2,
fusc(M, F),
assertz(fusc_cache(N, F)).
fusc(N, F):-
N1 is (N - 1)//2,
N2 is (N + 1)//2,
fusc(N1, F1),
fusc(N2, F2),
F is F1 + F2,
assertz(fusc_cache(N, F)).

print_fusc_sequence(N):-
writef('First %w fusc numbers:\n', [N]),
print_fusc_sequence(N, 0),
nl.

print_fusc_sequence(N, M):-
M >= N,
!.
print_fusc_sequence(N, M):-
fusc(M, F),
writef('%w ', [F]),
M1 is M + 1,
print_fusc_sequence(N, M1).

print_max_fusc(N):-
writef('Fusc numbers up to %w that are longer than any previous one:\n', [N]),
print_max_fusc(N, 0, 0).

print_max_fusc(N, M, _):-
M >= N,
!.
print_max_fusc(N, M, Max):-
fusc(M, F),
(F >= Max ->
writef('n = %w, fusc(n) = %w\n', [M, F]), Max1 = max(10, Max * 10)
;
Max1 = Max
),
M1 is M + 1,
print_max_fusc(N, M1, Max1).

main:-
print_fusc_sequence(61),
print_max_fusc(1000000).
```
Output:
```First 61 fusc numbers:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
Fusc numbers up to 1000000 that are longer than any previous one:
n = 0, fusc(n) = 0
n = 37, fusc(n) = 11
n = 1173, fusc(n) = 108
n = 35499, fusc(n) = 1076
n = 699051, fusc(n) = 10946
```

## Python

### Procedural

```from collections import deque
from itertools import islice, count

def fusc():
q = deque()
yield 0
yield 1

while True:
x = q.popleft()
q.append(x)
yield x

x += q
q.append(x)
yield x

def longest_fusc():
sofar = 0
for i, f in zip(count(), fusc()):
if f >= sofar:
yield(i, f)
sofar = 10 * sofar or 10

print('First 61:')
print(list(islice(fusc(), 61)))

print('\nLength records:')
for i, f in islice(longest_fusc(), 6):
print(f'fusc({i}) = {f}')
```
Output:
```First 61:
[0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4]

Length records:
fusc(0) = 0
fusc(37) = 11
fusc(1173) = 108
fusc(35499) = 1076
fusc(699051) = 10946
fusc(19573419) = 103682```

### Functional

By composition of pure functions, avoiding mutable variables, and confining any unavoidables to the internals of well-tested primitives:

```'''Fusc sequence'''

from itertools import chain, count, islice
from operator import itemgetter

# As an infinite stream of terms,

# infiniteFusc :: [Int]
def infiniteFusc():
'''Fusc sequence.
OEIS A2487
'''
def go(step):
isEven, n, xxs = step
x, xs = xxs, xxs[1:]
if isEven:
nxt = n + x
return not isEven, nxt, xxs + [nxt]
else:
return not isEven, x, xs + [x]

return chain(
[0, 1],
map(
itemgetter(1),
iterate(go)(
(True, 1, )
)
)
)

# Or as a function over an integer:

# fusc :: Int -> Int
def fusc(i):
'''Fusc sequence'''
def go(n):
if 0 == n:
return (1, 0)
else:
x, y = go(n // 2)
return (x + y, y) if 0 == n % 2 else (
x, x + y
)
return 0 if 1 > i else (
go(i - 1)
)

# firstFuscOfEachMagnitude ::
def firstFuscOfEachMagnitude():
'''Non-finite stream of each term
in OEIS A2487 that requires an
unprecedented quantity of decimal digits.
'''
a2487 = enumerate(map(fusc, count()))

def go(e):
limit = 10 ** e
return next(
(i, x) for i, x in a2487
if limit <= x
)
return (
chain([(0, 0)], map(go, count(1)))
)

# --------------------------TEST---------------------------
# main :: IO ()
def main():
'''Tests'''

print('First 61 terms:')
print(showList(
take(61)(
map(fusc, count())
)
))

print('\nFirst term of each decimal magnitude:')
print('(Index, Term):')
ixs = firstFuscOfEachMagnitude()
for _ in range(0, 5):
print(next(ixs))

# -------------------------GENERIC-------------------------

# iterate :: (a -> a) -> a -> Gen [a]
def iterate(f):
'''An infinite list of repeated
applications of f to x.
'''
def go(x):
v = x
while True:
yield v
v = f(v)
return lambda x: go(x)

# showList :: [a] -> String
def showList(xs):
'''Compact stringification of a list.'''
return '[' + ','.join(repr(x) for x in xs) + ']'

# take :: Int -> [a] -> [a]
# take :: Int -> String -> String
def take(n):
'''The prefix of xs of length n,
or xs itself if n > length xs.
'''
return lambda xs: (
xs[0:n]
if isinstance(xs, (list, tuple))
else list(islice(xs, n))
)

# MAIN ---
if __name__ == '__main__':
main()
```
Output:
```First 61 terms:
[0,1,1,2,1,3,2,3,1,4,3,5,2,5,3,4,1,5,4,7,3,8,5,7,2,7,5,8,3,7,4,5,1,6,5,9,4,11,7,10,3,11,8,13,5,12,7,9,2,9,7,12,5,13,8,11,3,10,7,11,4]

First term of each decimal magnitude:
(Index, Term):
(0, 0)
(37, 11)
(1173, 108)
(35499, 1076)
(699051, 10946)```

## Quackery

```  [ 1 & ]                is odd       ( n --> b )

[ 0 swap
[ dip 1+
10 / dup
0 = until ]
drop ]               is digits    ( n --> n )

[ dup dup size
dup odd iff
[ dup 1 - 2 /
dip
[ 1 + 2 / peek
over ]
peek + ]
else
[ 2 / peek ]
join ]               is nextfusc  ( [ --> [ )

say "First 61 terms." cr
' [ 0 1 ]
59 times nextfusc
witheach [ echo sp ]
cr cr
say "Terms where the digit count increases." cr
say "fusc(0) = 0" cr
1 ' [ 0 1 ]
[ nextfusc
dup -1 peek digits
rot 2dup > iff
[ drop swap
say "fusc("
dup -1 peek echo
say ") = "
dup size 1 - echo cr ]
else [ nip swap ]
dup size 1000000 = until ]
2drop```
Output:
```First 61 terms.
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

Terms where the digit count increases.
fusc(0) = 0
fusc(11) = 37
fusc(108) = 1173
fusc(1076) = 35499
fusc(10946) = 699051```

## R

I believe that this code demonstrates a great truth of R: It is amazing with numbers, but terrible with strings. There is really no good reason why checking how long a number is and printing it nicely should be hardest parts of this task.

Our first step is to adapt the 0-indexed definition to our 1-indexed language, letting us complete the first task.

```firstNFuscNumbers <- function(n)
{
stopifnot(n > 0)
if(n == 1) return(0) else fusc <- c(0, 1)
if(n > 2)
{
for(i in seq(from = 3, to = n, by = 1))
{
fusc[i] <- if(i %% 2) fusc[(i + 1) / 2] else fusc[i / 2] + fusc[(i + 2) / 2]
}
}
fusc
}
first61 <- firstNFuscNumbers(61)
cat("The first 61 Fusc numbers are:", "\n", first61, "\n")
```

The second task's requirements are somewhat strange. It asks for the number, implying that there is only one, but it is clear that there are several. If we only want the first such number, then the task is trivial. As we have already seen it in the n=61 output, we don't even have to be smart. Indeed, if we were being smart, we'd say that the answer was trivial: 0 at index 1.

A proper solution that only gives one non-trivial result is as follows:

```index <- which.max(nchar(first61) == 2)
number <- first61[index]
cat("The first fusc number that is longer than all previous fusc numbers is", number,
"and it occurs at index", index, "\n")
```

Regardless, as many of the other solutions have displayed many such numbers (e.g. the 6 digit case), we will do the same. This complicates matters in some unexpected ways. For example, nchar misbehaves once its inputs get large enough for R to default to scientific notation. One nice solution is to use format, which also allows us to add the required commas:

```twentyMillion <- firstNFuscNumbers(2 * 10^7)
twentyMillionCountable <- format(twentyMillion, scientific = FALSE, trim = TRUE)
indices <- sapply(2:6, function(x) which.max(nchar(twentyMillionCountable) == x))
numbers <- twentyMillion[indices]
cat("Some fusc numbers that are longer than all previous fusc numbers are:\n",
paste0(format(twentyMillion[indices], scientific = FALSE, trim = TRUE, big.mark = ","),
" (at index ", format(indices, trim = TRUE, big.mark = ","), ")\n"))
```
Output:
```The first 61 Fusc numbers are:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
The first fusc number that is longer than all previous fusc numbers is 11 and it occurs at index 38
Some fusc numbers that are longer than all previous fusc numbers are:
11 (at index 38)
108 (at index 1,174)
1,076 (at index 35,500)
10,946 (at index 699,052)
103,682 (at index 19,573,420)```

## Racket

```#lang racket

(require racket/generator)

(define (memoize f)
(define table (make-hash))
(λ args (hash-ref! table args (thunk (apply f args)))))

(define fusc
(memoize
(λ (n)
(cond
[(<= n 1) n]
[(even? n) (fusc (/ n 2))]
[else (+ (fusc (/ (sub1 n) 2)) (fusc (/ (add1 n) 2)))]))))

(define (comma x)
(string-join
(reverse
(for/list ([digit (in-list (reverse (string->list (~a x))))] [i (in-naturals)])
(cond
[(and (= 0 (modulo i 3)) (> i 0)) (string digit #\,)]
[else (string digit)])))
""))

(displayln (string-join (for/list ([i (in-range 61)]) (comma (fusc i))) " "))
(newline)

(define gen
(in-generator
(let loop ([prev 0] [i 0])
(define result (fusc i))
(define len (string-length (~a result)))
(cond
[(> len prev)
(yield (list i result))

(for ([i (in-range 5)] [x gen])
(match-define (list index result) x)
(printf "~a: ~a\n" (comma index) (comma result)))
```
Output:
```0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

0: 0
37: 11
1,173: 108
35,499: 1,076
699,051: 10,946
```

## Raku

(formerly Perl 6)

### Recurrence

```my @Fusc = 0, 1, 1, { |(@Fusc[\$_ - 1] + @Fusc[\$_], @Fusc[\$_]) given ++\$+1 } ... *;

sub comma { \$^i.flip.comb(3).join(',').flip }

put "First 61 terms of the Fusc sequence:\n{@Fusc[^61]}" ~
"\n\nIndex and value for first term longer than any previous:";

for flat 'Index', 'Value', 0, 0, (1..4).map({
my \$l = 10**\$_;
@Fusc.first(* > \$l, :kv).map: &comma
}) -> \$i, \$v {
printf "%15s : %s\n", \$i, \$v
}
```
Output:
```First 61 terms of the Fusc sequence:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

Index and value for first term longer than any previous:
Index : Value
0 : 0
37 : 11
1,173 : 108
35,499 : 1,076
699,051 : 10,946
```

### Recursive

Alternative version using Raku's multiple-dispatch feature. This version is significantly slower than the one above, but it's definitely prettier.

```multi fusc( 0 ) { 0 }
multi fusc( 1 ) { 1 }
multi fusc( \$n where \$n %% 2 ) { fusc \$n div 2 }
multi fusc( \$n ) { [+] map *.&fusc, ( \$n - 1 ) div 2, ( \$n + 1 ) div 2 }
put map *.&fusc, 0..60;
```
Output:
`0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4`

## REXX

### version 1, standard formatting

```/*REXX program  calculates and displays the   fusc   (or  Stern's Diatomic)   sequence. */
parse arg st # xw .                              /*obtain optional arguments from the CL*/
if st=='' | st==","  then st=  0                 /*Not specified?  Then use the default.*/
if  #=='' |  #==","  then  #= 61                 /* "      "         "   "   "     "    */
if xw=='' | xw==","  then xw=  0                 /* "      "         "   "   "     "    */
list= xw<1                                       /*boolean value:  LIST  to show numbers*/
@.=;        @.0= 0;       @.1= 1                 /*assign array default; assign low vals*/
mL= 0                                            /*the maximum length (digits)  so far. */
\$=                                               /* "  list of  fusc  numbers    "  "   */
do j=0  for #                                 /*process a bunch of integers from zero*/
if j>1  then if j//2  then do;  _= (j-1) % 2;   p= (j+1) % 2;   @.j= @._ + @.p;   end
else do;  _= j % 2;                       @.j= @._;         end
if list  then if j>=st  then \$= \$ commas(@.j)                      /*add it to a list*/
else nop                                   /*NOP≡placeholder.*/
else do;   if length(@.j)<=mL  then iterate               /*still too small.*/
mL= length(@.j)                                /*found increase. */
if mL==1  then say '═══index═══   ═══fusc number═══'
say right( commas(j), 9)     right( commas(@.j), 14)
if mL==xw  then leave     /*Found max length?  Then stop looking.*/
end                             /* [↑]  display fusc #s of maximum len.*/
end   /*j*/
/*\$   has a superfluous leading blank. */
if \$\==''  then say strip(\$)                     /*display a horizontal list of fusc #s.*/
exit 0                                           /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas:  parse arg ?;  do _=length(?)-3  to 1  by -3; ?=insert(',', ?, _); end;   return ?
```
output   when using the default inputs:
```0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
```
output   when using the default inputs:     ,   999999999   5
```═══index═══   ═══fusc number═══
0              0
37             11
1,173            108
35,499          1,076
699,051         10,946
```

### version 2, formatted with rows re─starting whenever a 1 (unity) appears

```/*REXX program  calculates and displays the   fusc   (or  Stern's Diatomic)   sequence. */
parse arg st # xw .                              /*obtain optional arguments from the CL*/
if st=='' | st==","  then st=   0                /*Not specified?  Then use the default.*/
if  #=='' |  #==","  then  #= 256                /* "      "         "   "   "     "    */
if xw=='' | xw==","  then xw=   0                /* "      "         "   "   "     "    */
list= xw<1                                       /*boolean value:  LIST  to show numbers*/
@.=;        @.0= 0;       @.1= 1                 /*assign array default; assign low vals*/
mL= 0                                            /*the maximum length (digits)  so far. */
\$=                                               /* "  list of  fusc  numbers    "  "   */
do j=0  for #                                 /*process a bunch of integers from zero*/
if j>1  then if j//2  then do;  _= (j-1) % 2;   p= (j+1) % 2;   @.j= @._ + @.p;   end
else do;  _= j % 2;                       @.j= @._;         end
if list  then if j>=st  then \$= \$ commas(@.j)                      /*add it to a list*/
else nop                                   /*NOP≡placeholder.*/
else do;   if length(@.j)<=mL  then iterate               /*still too small.*/
mL= length(@.j)                                /*found increase. */
if mL==1  then say '═══index═══   ═══fusc number═══'
say right( commas(j), 9)     right( commas(@.j), 14)
if mL==xw  then leave     /*Found max length?  Then stop looking.*/
end                             /* [↑]  display fusc #s of maximum len.*/
end   /*j*/
/*\$   has a superfluous leading blank. */
if \$==''  then exit 0                            /*display a horizontal list of fusc #s.*/
row= -1                                          /*output will be starting ar row  zero.*/
\$\$= 0                                            /*initialize with the zeroth entry (=0)*/
do k=2  for #;       y= word(\$, k)        /*start processing with the 2nd number.*/
if y==1  then do;  row= row + 1           /*Is it unity?    Then bump row number.*/
say 'row('row")="  \$\$  /*display the row that was just created*/
\$\$= 1                  /*initialize a new row with 1  (unity).*/
end
else \$\$= \$\$  y                   /*Not unity?   Just append it to a row.*/
end   /*k*/

if \$\$\==''  then say "row("row+1')='  \$\$         /*display any residual data in the row.*/
exit 0                                           /*stick a fork in it,  we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas:  parse arg ?;  do _=length(?)-3  to 1  by -3; ?=insert(',', ?, _); end;   return ?
```
output   when using the default inputs:

(Shown at  70%  size.)

```row(0)= 0
row(1)= 1
row(2)= 1 2
row(3)= 1 3 2 3
row(4)= 1 4 3 5 2 5 3 4
row(5)= 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5
row(6)= 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4 9 5 6
row(7)= 1 7 6 11 5 14 9 13 4 15 11 18 7 17 10 13 3 14 11 19 8 21 13 18 5 17 12 19 7 16 9 11 2 11 9 16 7 19 12 17 5 18 13 21 8 19 11 14 3 13 10 17 7 18 11 15 4 13 9 14 5 11 6 7
row(8)= 1 8 7 13 6 17 11 16 5 19 14 23 9 22 13 17 4 19 15 26 11 29 18 25 7 24 17 27 10 23 13 16 3 17 14 25 11 30 19 27 8 29 21 34 13 31 18 23 5 22 17 29 12 31 19 26 7 23 16 25 9 20 11 13 2 13 11 20 9 25 16 23 7 26 19 31 12 29 17 22 5 23 18 31 13 34 21 29 8 27 19 30 11 25 14 17 3 16 13 23 10 27 17 24 7 25 18 29 11 26 15 19 4 17 13 22 9 23 14 19 5 16 11 17 6 13 7 8
```
Output observation:   note that each (positive) row doubles in size (number of entries),   and starts with unity (1),   and
ends with the number of the row   (if the number of sequence elements is a power of two).

## Ring

```# Project: Fusc sequence

max = 60
fusc = list(36000)
fusc = 1
see "working..." + nl
see "wait for done..." + nl
see "The first 61 fusc numbers are:" + nl
fuscseq(max)
see "0"
for m = 1 to max
see " " + fusc[m]
next

see nl
see "The fusc numbers whose length > any previous fusc number length are:" + nl
see "Index Value" + nl
see " 0     0" + nl
d = 10
for i = 1 to 36000
if fusc[i] >= d
see " " + i + "   " + fusc[i] + nl
if d = 0
d = 1
ok
d = d*10
ok
next
see "done..." + nl

func fuscseq(max)
for n = 2 to 36000
if n%2 = 1
fusc[n] = fusc[(n-1)/2] + fusc[(n+1)/2]
but n%2 = 0
fusc[n] = fusc[n/2]
ok
next```
Output:
```working...
wait for done...
The first 61 fusc numbers are:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
The fusc numbers whose length > any previous fusc number length are:
Index Value
0     0
37    11
1173  108
35499 1076
done...
```

## Ruby

Using two Enumerators; the second making use of the first:

```fusc = Enumerator.new do |y|
y << 0
y << 1
arr = [0,1]
2.step do |n|
res = n.even? ? arr[n/2] : arr[(n-1)/2] + arr[(n+1)/2]
y   << res
arr << res
end
end

fusc_max_digits = Enumerator.new do |y|
cur_max, cur_exp = 0, 0
0.step do |i|
f = fusc.next
if f >= cur_max
cur_exp += 1
cur_max = 10**cur_exp
y << [i, f]
end
end
end

puts fusc.take(61).join(" ")
fusc_max_digits.take(6).each{|pair| puts "%15s : %s" % pair }
```
Output:
```0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
0 : 0
11 : 37
108 : 1173
1076 : 35499
10946 : 699051
103682 : 19573419
```

## Rust

```fn fusc_sequence() -> impl std::iter::Iterator<Item = u32> {
let mut sequence = vec![0, 1];
let mut n = 0;
std::iter::from_fn(move || {
if n > 1 {
sequence.push(match n % 2 {
0 => sequence[n / 2],
_ => sequence[(n - 1) / 2] + sequence[(n + 1) / 2],
});
}
let result = sequence[n];
n += 1;
Some(result)
})
}

fn main() {
println!("First 61 fusc numbers:");
for n in fusc_sequence().take(61) {
print!("{} ", n)
}
println!();

let limit = 1000000000;
println!(
"Fusc numbers up to {} that are longer than any previous one:",
limit
);
let mut max = 0;
for (index, n) in fusc_sequence().take(limit).enumerate() {
if n >= max {
max = std::cmp::max(10, max * 10);
println!("index = {}, fusc number = {}", index, n);
}
}
}
```
Output:
```First 61 fusc numbers:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
Fusc numbers up to 1000000000 that are longer than any previous one:
index = 0, fusc number = 0
index = 37, fusc number = 11
index = 1173, fusc number = 108
index = 35499, fusc number = 1076
index = 699051, fusc number = 10946
index = 19573419, fusc number = 103682
index = 615164587, fusc number = 1010747
```

## Sidef

```func fusc(n) is cached {

return 0 if n.is_zero
return 1 if n.is_one

n.is_even ? fusc(n/2) : (fusc((n-1)/2) + fusc(((n-1)/2)+1))
}

say ("First 61 terms of the Stern-Brocot sequence: ", 61.of(fusc).join(' '))

say "\nIndex and value for first term longer than any previous:"
printf("%15s : %s\n", "Index", "Value");

var (index=0, len=0)

5.times {
index = (index..Inf -> first_by { fusc(_).len > len })
len = fusc(index).len
printf("%15s : %s\n", index.commify, fusc(index).commify)
}
```
Output:
```First 61 terms of the Stern-Brocot sequence: 0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

Index and value for first term longer than any previous:
Index : Value
0 : 0
37 : 11
1,173 : 108
35,499 : 1,076
699,051 : 10,946
```

## Swift

```struct FuscSeq: Sequence, IteratorProtocol {
private var arr = [0, 1]
private var i = 0

mutating func next() -> Int? {
defer {
i += 1
}

guard i > 1 else {
return arr[i]
}

switch i & 1 {
case 0:
arr.append(arr[i / 2])
case 1:
arr.append(arr[(i - 1) / 2] + arr[(i + 1) / 2])
case _:
fatalError()
}

return arr.last!
}
}

let first = FuscSeq().prefix(61)

print("First 61: \(Array(first))")

var max = -1

for (i, n) in FuscSeq().prefix(20_000_000).enumerated() {
let f = String(n).count

if f > max {
max = f

print("New max: \(i): \(n)")
}
}
```
Output:
```First 61: [0, 1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4]
New max: 0: 0
New max: 37: 11
New max: 1173: 108
New max: 35499: 1076
New max: 699051: 10946
New max: 19573419: 103682```

## Tcl

```proc fusc n {
if {\$n < 2} {
return \$n
}

if {[info exists ::g_fusc(\$n)]} { return \$::g_fusc(\$n) }

if {\$n % 2} {               ;# n is odd
set r [expr {[fusc [expr {(\$n-1)/2}]] + [fusc [expr {(\$n+1)/2}]]}]
} else {                    ;# n is even
set r [fusc [expr {\$n/2}]]
}

if {\$n < 999999} { set ::g_fusc(\$n) \$r }

return \$r
}

proc ,,, {str {sep ,} {grouplen 3}} {
set strlen [string length \$str]
set padlen [expr {(\$grouplen - (\$strlen % \$grouplen)) % \$grouplen}]
set r [regsub -all ... [string repeat " " \$padlen]\$str &\$sep]
return [string range \$r \$padlen end-[string length \$sep]]
}

proc tabline {a b c} {
puts "[format %2s \$a] [format %10s \$b] [format %8s \$c]"
}

proc doit {{nmax 20000000}} {
for {set i 0} {\$i < 61} {incr i} {
puts -nonewline " [fusc \$i]"
}
puts ""
tabline L n fusc(n)
set maxL 0
for {set n 0} {\$n < \$nmax} {incr n} {
set f [fusc \$n]
set L [string length \$f]
if {\$L > \$maxL} {
set maxL \$L
tabline \$L [,,, \$n] [,,, \$f]
}
}
}
doit
```
Output:
``` 0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
L          n  fusc(n)
1          0        0
2         37       11
3      1,173      108
4     35,499    1,076
5    699,051   10,946
6 19,573,419  103,682

real    2m5.559s
```

## uBasic/4tH

Translation of: C

Only numbers up to 35500 are listed, otherwise it would take an unreasonable amount of time to run this program.

```Print "Index-------Value"

For i = 0 To 60
Print Using "____#"; i; Using "___________#"; FUNC(_fusc(i))
Next

Proc _printLargeFuscs (35500)
End

_fusc
Param (1)

If (a@ = 0) + (a@ = 1) Then Return (a@)
If (a@ % 2) = 0 Then Return (FUNC(_fusc(a@/2)))
Return (FUNC(_fusc((a@ - 1)/2)) + FUNC(_fusc((a@ + 1)/2)))

_printLargeFuscs
Param (1)
Local (4)             '              (int) i, f, len, maxLen = 1

e@ = 1
Print "\n\nPrinting all largest Fusc numbers upto "; a@; "\nIndex-------Value"

For b@ = 0 To a@
c@ = FUNC(_fusc(b@))
d@ = Len(Str(c@))

If d@ > e@ Then
e@ = d@
Print Using "____#"; b@; Using "___________#"; c@
EndIf
Next
Return
```
Output:
```Index-------Value
0           0
1           1
2           1
3           2
4           1
5           3
6           2
7           3
8           1
9           4
10           3
11           5
12           2
13           5
14           3
15           4
16           1
17           5
18           4
19           7
20           3
21           8
22           5
23           7
24           2
25           7
26           5
27           8
28           3
29           7
30           4
31           5
32           1
33           6
34           5
35           9
36           4
37          11
38           7
39          10
40           3
41          11
42           8
43          13
44           5
45          12
46           7
47           9
48           2
49           9
50           7
51          12
52           5
53          13
54           8
55          11
56           3
57          10
58           7
59          11
60           4

Printing all largest Fusc numbers upto 35500
Index-------Value
37          11
1173         108
35499        1076

0 OK, 0:145```

## Vala

Translation of: Nim
```int fusc(int n) {
if (n == 0 || n == 1)
return n;
else if (n % 2 == 0)
return fusc(n / 2);
else
return fusc((n - 1) / 2) + fusc((n + 1) / 2);
}

void main() {
print("The first 61 fusc numbers:\n");
for (int i = 0; i < 61; i++)
print(@"\$(fusc(i)) ");
print("\n\nThe fusc numbers whose lengths are greater than those of previous fusc numbers:\n");
print("        n   fusc(n)\n");
print("-------------------\n");
var max_length = 0;
for (int i = 0; i < 700000; i++) {
var f = fusc(i);
var length = f.to_string().length;
if (length > max_length) {
max_length = length;
print("%9d %9d\n", i, f);
}
}
}
```
Output:
```The first 61 fusc numbers:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

The fusc numbers whose lengths are greater than those of previous fusc numbers:
n   fusc(n)
-------------------
0         0
37        11
1173       108
35499      1076
699051     10946
```

## Visual Basic .NET

Translation of: C#
```Module Module1

Dim n As Integer = 61, l As List(Of Integer) = {0, 1}.ToList

Function fusc(n As Integer) As Integer
If n < l.Count Then Return l(n)
fusc = If((n And 1) = 0, l(n >> 1), l((n - 1) >> 1) + l((n + 1) >> 1))
End Function

Sub Main(args As String())
Dim lst As Boolean = True, w As Integer = -1, c As Integer = 0,
fs As String = "{0,11:n0}  {1,-9:n0}", res As String = ""
Console.WriteLine("First {0} numbers in the fusc sequence:", n)
For i As Integer = 0 To Integer.MaxValue
Dim f As Integer = fusc(i)
If lst Then
If i < 61 Then
Console.Write("{0} ", f)
Else
lst = False
Console.WriteLine()
Console.WriteLine("Points in the sequence where an item has more digits than any previous items:")
Console.WriteLine(fs, "Index\", "/Value") : Console.WriteLine(res) : res = ""
End If
End If
Dim t As Integer = f.ToString.Length
If t > w Then
w = t
res &= If(res = "", "", vbLf) & String.Format(fs, i, f)
If Not lst Then Console.WriteLine(res) : res = ""
c += 1 : If c > 5 Then Exit For
End If
Next : l.Clear()
End Sub
End Module
```
Output:
```First 61 numbers in the fusc sequence:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
Points in the sequence where an item has more digits than any previous items:
Index\  /Value
0  0
37  11
1,173  108
35,499  1,076
699,051  10,946
19,573,419  103,682
```

## Wren

Library: Wren-fmt
```import "/fmt" for Fmt

System.print("The first 61 numbers in the fusc sequence are:")
var fusc = [0, 1]
var fusc2 = [[0, 0]]
var maxLen = 1
var n = 2
while (n < 20e6) { // limit to indices under 20 million say
var f  = (n % 2  == 0) ? fusc[n/2] : fusc[(n-1)/2] + fusc[(n+1)/2]
var len = "%(f)".count
if (len > maxLen) {
maxLen = len
if (n <= 60) {
} else {
System.print("%(Fmt.dc(10, n))  %(Fmt.dc(0, f))")
}
}
if (n == 60 ) {
for (f in fusc) System.write("%(f) ")
System.print("\n\nFirst terms longer than any previous ones for indices < 20,000,000:")
System.print("     Index  Value")
for (iv in fusc2) System.print("%(Fmt.d(10, iv))  %(iv)")
}
n = n + 1
}
```
Output:
```The first 61 numbers in the fusc sequence are:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

First terms longer than any previous ones for indices < 20,000,000:
Index  Value
0  0
37  11
1,173  108
35,499  1,076
699,051  10,946
19,573,419  103,682
```

## XPL0

```func IntLen(N); \Return number of digits in N
int  N, L;
[L:= 0;
repeat  N:= N/10;
L:= L+1;
until   N = 0;
return L;
];

def Size = 1000000;
int Fusc(Size), N, Len, Max;
[Fusc(0):= 0;  Fusc(1):= 1;
for N:= 2 to Size-1 do
Fusc(N):= if N&1 then Fusc((N-1)/2) + Fusc((N+1)/2) else Fusc(N/2);
for N:= 0 to 60 do
[IntOut(0, Fusc(N));  ChOut(0, ^ )];
Text(0, "
n       fusc(n)
");
Max:= 0;
for N:= 0 to Size-1 do
[Len:= IntLen(Fusc(N));
if Len > Max then
[Max:= Len;
IntOut(0, N);  ChOut(0, 9\tab\);
IntOut(0, Fusc(N));  CrLf(0);
];
];
]```
Output:
```0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4
n       fusc(n)
0       0
37      11
1173    108
35499   1076
699051  10946
```

## Yabasic

```maximo = 20000000
dim f(maximo)

fusc()

for i = 0 to 60
print f(i), " ";
next i

print "\n\n      Index       Value"
d = 0
for i = 0 to maximo-1
if f(i) >= d then
print i using "###,###,###", f(i) using "###,###,###"
if d = 0 d = 1
d = d * 10
end if
next i
end

sub fusc()
f(0) = 0 : f(1) = 1
for n = 2 to maximo-1
if mod(n, 2) then
f(n) = f((n-1) / 2) + f((n+1) / 2)
else
f(n) = f(n / 2)
end if
next n
end sub
```
Output:
`Igual que la entrada de FreeBASIC.`

## zkl

```fuscs:=List.createLong(1_000_000, 0); fuscs=1; // we'll just use a big count
foreach n in ([2..fuscs.len()-1]){		 // and generate
fuscs[n]=( if(n.isEven()) fuscs[n/2] else fuscs[(n-1)/2] + fuscs[(n+1)/2] )
}

println("First 61 terms of the Stern-Brocot sequence:");
fuscs[0,61].concat(" ").println();

println("\nIndex and value for first term longer than any previous:");
println("          Index : Value");
prevMax:=-1;
foreach n in (fuscs.len()){
f,fd := fuscs[n], f.numDigits;
if(fd>prevMax){ println("%15,d : %,d".fmt(n,f)); prevMax=fd }
}```
Output:
```First 61 terms of the Stern-Brocot sequence:
0 1 1 2 1 3 2 3 1 4 3 5 2 5 3 4 1 5 4 7 3 8 5 7 2 7 5 8 3 7 4 5 1 6 5 9 4 11 7 10 3 11 8 13 5 12 7 9 2 9 7 12 5 13 8 11 3 10 7 11 4

Index and value for first term longer than any previous:
Index : Value
0 : 0
37 : 11
1,173 : 108
35,499 : 1,076
699,051 : 10,946
```