Numbers whose binary and ternary digit sums are prime
Show positive integers n whose binary and ternary digits sum are prime, where n < 200.
Numbers whose binary and ternary digit sums are prime is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
- Task
11l
F is_prime(a)
I a == 2
R 1B
I a < 2 | a % 2 == 0
R 0B
L(i) (3 .. Int(sqrt(a))).step(2)
I a % i == 0
R 0B
R 1B
F digit_sum(=n, b)
V result = 0
L n != 0
result += n % b
n I/= b
R result
V count = 0
L(n) 2..199
I is_prime(digit_sum(n, 2)) &
is_prime(digit_sum(n, 3))
count++
print(‘#3’.format(n), end' I count % 16 == 0 {"\n"} E ‘ ’)
print()
print(‘Found ’count‘ numbers.’)- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 Found 61 numbers.
Action!
INCLUDE "H6:SIEVE.ACT"
BYTE Func IsPrime(INT i BYTE base BYTE ARRAY primes)
BYTE sum,d
sum=0
WHILE i#0
DO
d=i MOD base
sum==+d
i==/base
OD
RETURN (primes(sum))
PROC Main()
DEFINE MAX="199"
BYTE ARRAY primes(MAX+1)
INT i,count=[0]
Put(125) PutE() ;clear the screen
Sieve(primes,MAX+1)
FOR i=1 TO MAX
DO
IF IsPrime(i,2,primes)=1 AND IsPrime(i,3,primes)=1 THEN
PrintI(i) Put(32)
count==+1
FI
OD
PrintF("%E%EThere are %I numbers",count)
RETURN- Output:
Screenshot from Atari 8-bit computer
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 14 5 151 155 157 162 167 171 173 179 181 185 191 193 199 There are 61 numbers
ALGOL 68
BEGIN # find numbers whose digit sums in binary and ternary are prime #
# returns the digit sum of n in base b #
PRIO DIGITSUM = 9;
OP DIGITSUM = ( INT n, b )INT:
BEGIN
INT d sum := 0;
INT v := ABS n;
WHILE v > 0 DO
d sum +:= v MOD b;
v OVERAB b
OD;
d sum
END # DIGITSUM # ;
PR read "primes.incl.a68" PR
[]BOOL prime = PRIMESIEVE 200;
INT n count := 0;
FOR n TO UPB prime DO
INT d sum 2 = n DIGITSUM 2;
IF prime[ d sum 2 ] THEN
INT d sum 3 = n DIGITSUM 3;
IF prime[ d sum 3 ] THEN
# the base 2 and base 3 digit sums of n are both prime #
print( ( " ", whole( n, -3 ), IF prime[ n ] THEN "*" ELSE " " FI ) );
n count +:= 1;
IF n count MOD 14 = 0 THEN print( ( newline ) ) FI
FI
FI
OD;
print( ( newline ) );
print( ( "Found ", whole( n count, 0 ) ) );
print( ( " numbers whose binary and ternary digit sums are prime", newline ) );
print( ( " those that are themselves prime are suffixed with a ""*""", newline ) )
END- Output:
5* 6 7* 10 11* 12 13* 17* 18 19* 21 25 28 31*
33 35 36 37* 41* 47* 49 55 59* 61* 65 67* 69 73*
79* 82 84 87 91 93 97* 103* 107* 109* 115 117 121 127*
129 131* 133 137* 143 145 151* 155 157* 162 167* 171 173* 179*
181* 185 191* 193* 199*
Found 61 numbers whose binary and ternary digit sums are prime
those that are themselves prime are suffixed with a "*"
ALGOL-M
begin
integer function mod(a,b);
integer a,b;
mod := a-(a/b)*b;
integer function digitsum(n,base);
integer n,base;
digitsum := if n=0 then 0 else mod(n,base)+digitsum(n/base,base);
integer function isprime(n);
integer n;
begin
integer i;
isprime := 0;
if n < 2 then go to stop;
for i := 2 step 1 until n-1 do
begin
if mod(n,i) = 0 then go to stop;
end;
isprime := 1;
stop:
i := i;
end;
integer i,d2,d3,n;
n := 0;
for i := 0 step 1 until 199 do
begin
d2 := digitsum(i,2);
d3 := digitsum(i,3);
if isprime(d2) <> 0 and isprime(d3) <> 0 then
begin
if n/10 <> (n-1)/10 then write(i) else writeon(i);
n := n + 1;
end;
end;
end- Output:
5 6 7 10 11 12 13 17 18 19
21 25 28 31 33 35 36 37 41 47
49 55 59 61 65 67 69 73 79 82
84 87 91 93 97 103 107 109 115 117
121 127 129 131 133 137 143 145 151 155
157 162 167 171 173 179 181 185 191 193
199
ALGOL W
begin % find numbers whose binary and ternary digit sums are prime %
% returns the digit sum of n in base b %
integer procedure digitSum( integer value n, base ) ;
begin
integer v, dSum;
v := abs n;
dSum := 0;
while v > 0 do begin
dSum := dSum + v rem base;
v := v div base
end while_v_gt_0 ;
dSum
end digitSum ;
integer MAX_PRIME, MAX_NUMBER;
MAX_PRIME := 199;
begin
logical array prime( 1 :: MAX_PRIME );
integer nCount;
% sieve the primes to MAX_PRIME %
prime( 1 ) := false; prime( 2 ) := true;
for i := 3 step 2 until MAX_PRIME do prime( i ) := true;
for i := 4 step 2 until MAX_PRIME do prime( i ) := false;
for i := 3 step 2 until truncate( sqrt( MAX_PRIME ) ) do begin
integer ii; ii := i + i;
if prime( i ) then for np := i * i step ii until MAX_PRIME do prime( np ) := false
end for_i ;
% find the numbers %
nCount := 0;
for i := 1 until MAX_PRIME do begin
if prime( digitSum( i, 2 ) ) and prime( digitSum( i, 3 ) ) then begin
% have another matching number %
writeon( i_w := 3, s_w := 0, " ", i );
nCount := nCount + 1;
if nCount rem 14 = 0 then write()
end if_have_a_suitable_number
end for_i ;
write( i_w := 1, s_w := 0, "Found ", nCount, " numbers with prime binary and ternary digit sums up to ", MAX_PRIME )
end
end.- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 Found 61 numbers with prime binary and ternary digit sums up to 199
APL
(⊢(/⍨)(∧/((2=0+.=⍳|⊢)¨2 3(+/⊥⍣¯1)¨⊢))¨) ⍳200
- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117
121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
Arturo
loop split.every: 10
select 1..199 'n [ and? prime? sum digits.base: 2 n
prime? sum digits.base: 3 n ] 'a ->
print map a => [pad to :string & 4]
- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
AWK
# syntax: GAWK -f NUMBERS_WHICH_BINARY_AND_TERNARY_DIGIT_SUM_ARE_PRIME.AWK
# converted from C
BEGIN {
start = 0
stop = 199
for (i=start; i<=stop; i++) {
if (is_prime(sum_digits(i,2)) && is_prime(sum_digits(i,3))) {
printf("%4d%1s",i,++count%10?"":"\n")
}
}
printf("\nBinary and ternary digit sums are both prime %d-%d: %d\n",start,stop,count)
exit(0)
}
function sum_digits(n,base, sum) {
do {
sum += n % base
} while (n = int(n/base))
return(sum)
}
function is_prime(x, i) {
if (x <= 1) {
return(0)
}
for (i=2; i<=int(sqrt(x)); i++) {
if (x % i == 0) {
return(0)
}
}
return(1)
}
- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 Binary and ternary digit sums are both prime 0-199: 61
BASIC
Chipmunk Basic
100 rem Numbers which binary and ternary digit sum are prime
110 for n = 2 to 199
120 if is_prime(digit_sum(n,2)) <> 0 then
130 if is_prime(digit_sum(n,3)) <> 0 then print using "### ";n;
140 endif
150 next n
160 print
170 end
180 sub is_prime(p)
190 if p = 3 or p = 2 then
200 is_prime = 1
210 else
220 if p = 1 then
230 is_prime = 0
240 else
250 q = 1 : i = 1
260 i = i+1
270 if p mod i = 0 then q = 0
280 if i*i <= p and q <> 0 then 260
290 is_prime = q
300 endif
310 endif
320 end sub
330 sub digit_sum(n,bas)
340 p = 0 : xn = n
350 while xn <> 0
360 p = p+xn mod bas
370 xn = int(xn/bas)
380 wend
390 digit_sum = p
400 end sub
- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
FreeBASIC
#include"isprime.bas"
function digsum( byval n as uinteger, b as const uinteger ) as uinteger
'finds the digit sum of n in base b
dim as uinteger sum = 0
while n
sum+=n mod b
n\=b
wend
return sum
end function
for n as uinteger = 1 to 200
if isprime(digsum(n,2)) and isprime(digsum(n,3)) then print n;" ";
next n : print
- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
GW-BASIC
10 REM Numbers which binary and ternary digit sum are prime
20 FOR N = 2 TO 199
30 B = 2
40 GOSUB 200: GOSUB 120
50 IF Q = 0 THEN GOTO 90
60 B = 3
70 GOSUB 200: GOSUB 120
80 IF Q = 1 THEN PRINT USING "### ";N;
90 NEXT N
100 PRINT
110 END
120 REM tests if a number is prime
130 IF P = 3 OR P = 2 THEN Q = 1: RETURN
140 IF P = 1 THEN Q = 0: RETURN
150 Q = 1: I = 1
160 I = I + 1
170 IF P MOD I = 0 THEN Q = 0
180 IF I * I <= P AND Q <> 0 THEN GOTO 160
190 RETURN
200 REM finds the digit sum of N in base B, returns P
210 P = 0: XN = N
220 WHILE XN <> 0
230 P = P + XN MOD B
240 XN = XN \ B
250 WEND
260 RETURN
- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
Another solution
None of the digit sums are higher than 9, so the easiest thing to do is to hardcode which ones are prime.
10 REM Numbers which binary and ternary digit sum are prime
20 DEFINT I,J,K,P
30 DIM P(9): DATA 0,1,1,0,1,0,1,0,0
40 FOR I=1 TO 9: READ P(I): NEXT
50 FOR I=0 TO 199
60 J=0: K=I
70 IF K>0 THEN J=J+K MOD 2: K=K\2: GOTO 70 ELSE IF P(J)=0 THEN 100
80 J=0: K=I
90 IF K>0 THEN J=J+K MOD 3: K=K\3: GOTO 90 ELSE IF P(J) THEN PRINT I,
100 NEXT I
110 END
- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
Tiny BASIC
This isn't a very interesting problem. The most illustrative part of this solution is that it only uses four variables; several have multiple purposes. Efficiency is important when the language has only 26 variable names in total.
REM B digital base input to sumdig, also output of primality routine
REM N input to sumdig routine
REM P input to primality routine, output of sumdig routine
REM T temp variable in sumdig routine, loop var in prime routine
LET N = 1
20 LET N = N + 1
LET B = 2
GOSUB 200
GOSUB 100
IF B = 0 THEN GOTO 30
LET B = 3
GOSUB 200
GOSUB 100
IF B = 1 THEN PRINT N
30 IF N < 200 THEN GOTO 20
END
100 REM PRIMALITY BY TRIAL DIVISION
LET B = 0
IF P = 1 THEN RETURN
LET B = 1
IF P = 2 THEN RETURN
LET T = 2
110 IF (P/T)*T = P THEN LET B = 0
IF B = 0 THEN RETURN
LET T = T + 1
IF T*T <= P THEN GOTO 110
RETURN
200 REM digital sum of N in base B
LET T = N
LET P = 0
210 IF T = 0 THEN RETURN
LET P = P + T - (T/B)*B
LET T = T/B
GOTO 210BCPL
get "libhdr"
let digitsum(n, base) =
n=0 -> 0, n rem base + digitsum(n/base, base)
let isprime(n) = valof
$( if n<2 then resultis false
for i=2 to n-1 do
if n rem i = 0 then resultis false
resultis true
$)
let accept(n) =
isprime(digitsum(n,2)) & isprime(digitsum(n,3))
let start() be
$( let c = 0
for i=0 to 199 do
if accept(i) do
$( writef("%I4",i)
c := c + 1
if c rem 10 = 0 then wrch('*N')
$)
wrch('*N')
$)- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
C
#include <stdio.h>
#include <stdint.h>
/* good enough for small numbers */
uint8_t prime(uint8_t n) {
uint8_t f;
if (n < 2) return 0;
for (f = 2; f < n; f++) {
if (n % f == 0) return 0;
}
return 1;
}
/* digit sum in given base */
uint8_t digit_sum(uint8_t n, uint8_t base) {
uint8_t s = 0;
do {s += n % base;} while (n /= base);
return s;
}
int main() {
uint8_t n, s = 0;
for (n = 0; n < 200; n++) {
if (prime(digit_sum(n,2)) && prime(digit_sum(n,3))) {
printf("%4d",n);
if (++s>=10) {
printf("\n");
s=0;
}
}
}
printf("\n");
return 0;
}
- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
CLU
prime = proc (n: int) returns (bool)
if n<2 then return(false) end
for i: int in int$from_to(2, n-1) do
if n//i=0 then return(false) end
end
return(true)
end prime
digit_sum = proc (n, base: int) returns (int)
sum: int := 0
while n>0 do
sum := sum + n//base
n := n/base
end
return(sum)
end digit_sum
start_up = proc ()
po: stream := stream$primary_output()
n: int := 0
for i: int in int$from_to(2, 199) do
s2: int := digit_sum(i,2)
s3: int := digit_sum(i,3)
if prime(s2) cand prime(s3) then
stream$putright(po, int$unparse(i), 4)
n := n + 1
if n // 20 = 0 then stream$putl(po, "") end
end
end
end start_up- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
Cowgol
include "cowgol.coh";
sub prime(n: uint8): (p: uint8) is
p := 0;
if n >= 2 then
var f: uint8 := 2;
while f < n loop
if n % f == 0 then
return;
end if;
f := f + 1;
end loop;
p := 1;
end if;
end sub;
sub digit_sum(n: uint8, base: uint8): (sum: uint8) is
sum := 0;
while n > 0 loop
sum := sum + n % base;
n := n / base;
end loop;
end sub;
var n: uint8 := 0;
while n < 200 loop;
if prime(digit_sum(n,2)) != 0 and prime(digit_sum(n,3)) != 0 then
print_i8(n);
print_nl();
end if;
n := n + 1;
end loop;- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
Delphi
function IsPrime(N: int64): boolean;
{Fast, optimised prime test}
var I,Stop: int64;
begin
if (N = 2) or (N=3) then Result:=true
else if (n <= 1) or ((n mod 2) = 0) or ((n mod 3) = 0) then Result:= false
else
begin
I:=5;
Stop:=Trunc(sqrt(N+0.0));
Result:=False;
while I<=Stop do
begin
if ((N mod I) = 0) or ((N mod (I + 2)) = 0) then exit;
Inc(I,6);
end;
Result:=True;
end;
end;
function SumDigitsByBase(N,Base: integer): integer;
{Sum all digits of N in the specified B}
var I: integer;
begin
Result:=0;
repeat
begin
I:=N mod Base;
Result:=Result+I;
N:=N div Base;
end
until N = 0;
end;
function IsBinaryTernaryPrime(N: integer): boolean;
{Test if sums of binary and ternary digits is prime}
var Sum2,Sum3: integer;
begin
Result:=IsPrime(SumDigitsByBase(N,2)) and
IsPrime(SumDigitsByBase(N,3));
end;
procedure ShowBinaryTernaryPrimes(Memo: TMemo);
{Show the Binary-Ternary sum primes of first 200 values}
var I,Cnt: integer;
var S: string;
begin
S:=''; Cnt:=0;
for I:=0 to 200-1 do
if IsBinaryTernaryPrime(I) then
begin
Inc(Cnt);
S:=S+Format('%8D',[I]);
If (Cnt mod 5)=0 then S:=S+CRLF;
end;
Memo.Lines.Add(S);
Memo.Lines.Add('Count= '+IntToStr(Cnt));
end;
- Output:
5 6 7 10 11
12 13 17 18 19
21 25 28 31 33
35 36 37 41 47
49 55 59 61 65
67 69 73 79 82
84 87 91 93 97
103 107 109 115 117
121 127 129 131 133
137 143 145 151 155
157 162 167 171 173
179 181 185 191 193
199
Count= 61
Elapsed Time: 3.322 ms.
EasyLang
fastfunc isprim num .
if num < 2
return 0
.
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
func digsum n b .
while n > 0
sum += n mod b
n = n div b
.
return sum
.
for i = 1 to 199
if isprim digsum i 2 = 1 and isprim digsum i 3 = 1
write i & " "
.
.
- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
F#
This task uses Extensible Prime Generator (F#)
// binary and ternary digit sums are prime: Nigel Galloway. April 16th., 2021
let fN2,fN3=let rec fG n g=function l when l<n->l+g |l->fG n (g+l%n)(l/n) in (fG 2 0, fG 3 0)
{0..200}|>Seq.filter(fun n->isPrime(fN2 n) && isPrime(fN3 n))|>Seq.iter(printf "%d "); printfn ""
- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 Real: 00:00:00.005
Factor
USING: combinators combinators.short-circuit formatting io lists
lists.lazy math math.parser math.primes sequences ;
: dsum ( n base -- sum ) >base [ digit> ] map-sum ;
: dprime? ( n base -- ? ) dsum prime? ;
: 23prime? ( n -- ? ) { [ 2 dprime? ] [ 3 dprime? ] } 1&& ;
: l23primes ( -- list ) 1 lfrom [ 23prime? ] lfilter ;
: 23prime. ( n -- )
{
[ ]
[ >bin ]
[ 2 dsum ]
[ 3 >base ]
[ 3 dsum ]
} cleave
"%-8d %-9s %-6d %-7s %d\n" printf ;
"Base 10 Base 2 (sum) Base 3 (sum)" print
l23primes [ 200 < ] lwhile [ 23prime. ] leach
- Output:
Base 10 Base 2 (sum) Base 3 (sum) 5 101 2 12 3 6 110 2 20 2 7 111 3 21 3 10 1010 2 101 2 11 1011 3 102 3 12 1100 2 110 2 13 1101 3 111 3 17 10001 2 122 5 18 10010 2 200 2 19 10011 3 201 3 21 10101 3 210 3 25 11001 3 221 5 28 11100 3 1001 2 31 11111 5 1011 3 33 100001 2 1020 3 35 100011 3 1022 5 36 100100 2 1100 2 37 100101 3 1101 3 41 101001 3 1112 5 47 101111 5 1202 5 49 110001 3 1211 5 55 110111 5 2001 3 59 111011 5 2012 5 61 111101 5 2021 5 65 1000001 2 2102 5 67 1000011 3 2111 5 69 1000101 3 2120 5 73 1001001 3 2201 5 79 1001111 5 2221 7 82 1010010 3 10001 2 84 1010100 3 10010 2 87 1010111 5 10020 3 91 1011011 5 10101 3 93 1011101 5 10110 3 97 1100001 3 10121 5 103 1100111 5 10211 5 107 1101011 5 10222 7 109 1101101 5 11001 3 115 1110011 5 11021 5 117 1110101 5 11100 3 121 1111001 5 11111 5 127 1111111 7 11201 5 129 10000001 2 11210 5 131 10000011 3 11212 7 133 10000101 3 11221 7 137 10001001 3 12002 5 143 10001111 5 12022 7 145 10010001 3 12101 5 151 10010111 5 12121 7 155 10011011 5 12202 7 157 10011101 5 12211 7 162 10100010 3 20000 2 167 10100111 5 20012 5 171 10101011 5 20100 3 173 10101101 5 20102 5 179 10110011 5 20122 7 181 10110101 5 20201 5 185 10111001 5 20212 7 191 10111111 7 21002 5 193 11000001 3 21011 5 199 11000111 5 21101 5
Fermat
Function Digsum(n, b) =
digsum := 0;
while n>0 do
digsum := digsum + n|b;
n:=n\b;
od;
digsum.;
for p=1 to 200 do
if Isprime(Digsum(p,3)) and Isprime(Digsum(p,2)) then
!(p,' ');
nadd := nadd+1;
fi od;- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
FOCAL
01.10 S P(2)=1;S P(3)=1;S P(5)=1;S P(7)=1
01.20 S V=10
01.30 F N=0,199;D 3
01.40 T !
01.50 Q
02.10 S A=0
02.20 S M=N
02.30 S T=FITR(M/B)
02.40 S A=A+M-T*B
02.50 S M=T
02.60 I (-M)2.3
03.10 S B=2;D 2;S X=A
03.20 S B=3;D 2;S Y=A
03.30 I (-P(X)*P(Y))3.4;R
03.40 T %4,N
03.50 S V=V-1
03.60 I (-V)3.7;T !;S V=10
03.70 R- Output:
= 5= 6= 7= 10= 11= 12= 13= 17= 18= 19 = 21= 25= 28= 31= 33= 35= 36= 37= 41= 47 = 49= 55= 59= 61= 65= 67= 69= 73= 79= 82 = 84= 87= 91= 93= 97= 103= 107= 109= 115= 117 = 121= 127= 129= 131= 133= 137= 143= 145= 151= 155 = 157= 162= 167= 171= 173= 179= 181= 185= 191= 193 = 199
Fōrmulæ
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Programs in Fōrmulæ are created/edited online in its website.
In this page you can see and run the program(s) related to this task and their results. You can also change either the programs or the parameters they are called with, for experimentation, but remember that these programs were created with the main purpose of showing a clear solution of the task, and they generally lack any kind of validation.
Solution
Go
package main
import (
"fmt"
"rcu"
)
func main() {
var numbers []int
for i := 2; i < 200; i++ {
bds := rcu.DigitSum(i, 2)
if rcu.IsPrime(bds) {
tds := rcu.DigitSum(i, 3)
if rcu.IsPrime(tds) {
numbers = append(numbers, i)
}
}
}
fmt.Println("Numbers < 200 whose binary and ternary digit sums are prime:")
for i, n := range numbers {
fmt.Printf("%4d", n)
if (i+1)%14 == 0 {
fmt.Println()
}
}
fmt.Printf("\n\n%d such numbers found\n", len(numbers))
}
- Output:
Numbers < 200 whose binary and ternary digit sums are prime: 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 61 such numbers found
Haskell
import Data.Bifunctor (first)
import Data.List.Split (chunksOf)
import Data.Numbers.Primes (isPrime)
--------- BINARY AND TERNARY DIGIT SUMS BOTH PRIME -------
digitSumsPrime :: Int -> [Int] -> Bool
digitSumsPrime n = all (isPrime . digitSum n)
digitSum :: Int -> Int -> Int
digitSum n base = go n
where
go 0 = 0
go n = uncurry (+) (first go $ quotRem n base)
--------------------------- TEST -------------------------
main :: IO ()
main =
putStrLn $
show (length xs)
<> " matches in [1..199]\n\n"
<> table xs
where
xs =
[1 .. 199]
>>= \x -> [show x | digitSumsPrime x [2, 3]]
------------------------- DISPLAY -----------------------
table :: [String] -> String
table xs =
let w = length (last xs)
in unlines $
unwords
<$> chunksOf
10
(justifyRight w ' ' <$> xs)
justifyRight :: Int -> Char -> String -> String
justifyRight n c = (drop . length) <*> (replicate n c <>)
61 matches in [1..199] 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
J
((1*./@p:2 3+/@(#.^:_1)"0])"0#]) i.200
- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
jq
Adapted from Wren
Also works with gojq, the Go implementation of jq, and with fq
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
def sum(s): reduce s as $_ (0; . + $_);
def is_prime:
. as $n
| if ($n < 2) then false
elif ($n % 2 == 0) then $n == 2
elif ($n % 3 == 0) then $n == 3
elif ($n % 5 == 0) then $n == 5
elif ($n % 7 == 0) then $n == 7
elif ($n % 11 == 0) then $n == 11
elif ($n % 13 == 0) then $n == 13
elif ($n % 17 == 0) then $n == 17
elif ($n % 19 == 0) then $n == 19
else 23
| until( (. * .) > $n or ($n % . == 0); .+2)
| . * . > $n
end;
def digitSum($base):
def stream:
recurse(if . > 0 then ./$base|floor else empty end) | . % $base ;
sum(stream);
def digit_sums_are_prime($n):
[range(2;$n)
| digitSum(2) as $bds
| select($bds|is_prime)
| digitSum(3) as $tds
| select($tds|is_prime) ];
def task($n):
"Numbers < \($n) whose binary and ternary digit sums are prime:",
(digit_sums_are_prime($n)
| length as $length
| (_nwise(14) | map(lpad(4)) | join(" ")),
"\nFound \($length) such numbers." );
task(200)- Output:
Numbers < 200 whose binary and ternary digit sums are prime: 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 Found 61 such numbers.
Julia
using Primes
btsumsareprime(n) = isprime(sum(digits(n, base=2))) && isprime(sum(digits(n, base=3)))
foreach(p -> print(rpad(p[2], 4), p[1] % 20 == 0 ? "\n" : ""), enumerate(filter(btsumsareprime, 1:199)))
- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
MAD
NORMAL MODE IS INTEGER
INTERNAL FUNCTION(P)
ENTRY TO PRIME.
WHENEVER P.L.2, FUNCTION RETURN 0B
THROUGH TEST, FOR DV=2, 1, DV.G.SQRT.(P)
TEST WHENEVER P-P/DV*DV.E.0, FUNCTION RETURN 0B
FUNCTION RETURN 1B
END OF FUNCTION
INTERNAL FUNCTION(N,BASE)
ENTRY TO DGTSUM.
SUM = 0
DN = N
DIGIT NX = DN/BASE
SUM = SUM + DN-NX*BASE
DN = NX
WHENEVER DN.G.0, TRANSFER TO DIGIT
FUNCTION RETURN SUM
END OF FUNCTION
THROUGH NBR, FOR I=0, 1, I.GE.200
WHENEVER PRIME.(DGTSUM.(I,2)) .AND. PRIME.(DGTSUM.(I,3))
PRINT FORMAT FMT, I
END OF CONDITIONAL
NBR CONTINUE
VECTOR VALUES FMT = $I3*$
END OF PROGRAM- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
Mathematica / Wolfram Language
Partition[
Select[
Range@
200, (PrimeQ[Total@IntegerDigits[#, 2]] &&
PrimeQ[Total@IntegerDigits[#, 3]]) &], UpTo[8]] // TableForm
- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
Nim
import strutils
func isPrime(n: Positive): bool =
if n == 1: return false
if n mod 2 == 0: return n == 2
if n mod 3 == 0: return n == 3
var d = 5
while d * d <= n:
if n mod d == 0: return false
inc d, 2
if n mod d == 0: return false
inc d, 4
return true
func digitSum(n, b: Natural): int =
var n = n
while n != 0:
result += n mod b
n = n div b
var count = 0
for n in 2..<200:
if digitSum(n, 2).isPrime and digitSum(n, 3).isPrime:
inc count
stdout.write ($n).align(3), if count mod 16 == 0: '\n' else: ' '
echo()
echo "Found ", count, " numbers."
- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 Found 61 numbers.
Perl
use strict;
use warnings;
use feature 'say';
use List::Util 'sum';
use ntheory <is_prime todigitstring>;
sub test_digits { 0 != is_prime sum split '', todigitstring(shift, shift) }
my @p;
test_digits($_,2) and test_digits($_,3) and push @p, $_ for 1..199;
say my $result = @p . " matching numbers:\n" . (sprintf "@{['%4d' x @p]}", @p) =~ s/(.{40})/$1\n/gr;
- Output:
61 matching numbers: 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
Phix
function to_base(atom n, integer base) string result = "" while true do result &= remainder(n,base) n = floor(n/base) if n=0 then exit end if end while return result end function function prime23(integer n) return is_prime(sum(to_base(n,2))) and is_prime(sum(to_base(n,3))) end function sequence res = filter(tagset(199),prime23) printf(1,"%d numbers found: %V\n",{length(res),shorten(res,"",5)})
- Output:
61 numbers found: {5,6,7,10,11,"...",181,185,191,193,199}
PL/I
PL/M
100H:
/* CP/M CALLS */
BDOS: PROCEDURE (FN, ARG); DECLARE FN BYTE, ARG ADDRESS; GO TO 5; END BDOS;
EXIT: PROCEDURE; CALL BDOS(0,0); END EXIT;
PRINT: PROCEDURE (S); DECLARE S ADDRESS; CALL BDOS(9,S); END PRINT;
/* PRINT NUMBER */
PRINT$NUMBER: PROCEDURE (N);
DECLARE S (8) BYTE INITIAL ('.....',13,10,'$');
DECLARE (N, P) ADDRESS, C BASED P BYTE;
P = .S(5);
DIGIT:
P = P - 1;
C = N MOD 10 + '0';
N = N / 10;
IF N > 0 THEN GO TO DIGIT;
CALL PRINT(P);
END PRINT$NUMBER;
/* SIMPLE PRIMALITY TEST */
PRIME: PROCEDURE (N) BYTE;
DECLARE (N, I) BYTE;
IF N < 2 THEN RETURN 0;
DO I=2 TO N-1;
IF N MOD I = 0 THEN RETURN 0;
END;
RETURN 1;
END PRIME;
/* SUM OF DIGITS */
DIGIT$SUM: PROCEDURE (N, BASE) BYTE;
DECLARE (N, BASE, SUM) BYTE;
SUM = 0;
DO WHILE N > 0;
SUM = SUM + N MOD BASE;
N = N / BASE;
END;
RETURN SUM;
END DIGIT$SUM;
/* TEST NUMBERS 0 .. 199 */
DECLARE I BYTE;
DO I=0 TO 199;
IF PRIME(DIGIT$SUM(I,2)) AND PRIME(DIGIT$SUM(I,3)) THEN
CALL PRINT$NUMBER(I);
END;
CALL EXIT;
EOF- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
See also #Polyglot:PL/I and PL/M
Plain English
To run:
Start up.
Loop.
If a counter is past 200, break.
If the counter has prime digit sums in binary and ternary, write the counter then " " on the console without advancing.
Repeat.
Wait for the escape key.
Shut down.
A sum is a number.
A base is a number.
To find a digit sum of a number given a base:
Privatize the number.
Loop.
Divide the number by the base giving a quotient and a remainder.
Add the remainder to the digit sum.
Put the quotient into the number.
If the number is 0, exit.
Repeat.
To decide if a number has prime digit sums in binary and ternary:
Find a digit sum of the number given 2.
If the digit sum is not prime, say no.
Find another digit sum of the number given 3.
If the other digit sum is not prime, say no.
Say yes.- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
Polyglot:PL/I and PL/M
... under CP/M (or an emulator)
Should work with many PL/I implementations.
The PL/I include file "pg.inc" can be found on the Polyglot:PL/I and PL/M page.
Note the use of text in column 81 onwards to hide the PL/I specifics from the PL/M compiler.
/* FIND NUMBERS WHOSE DIGIT SUM SQUARED AND CUBED IS PRIME */
prime_digit_sums_100H: procedure options (main);
/* PL/I DEFINITIONS */
%include 'pg.inc';
/* PL/M DEFINITIONS: CP/M BDOS SYSTEM CALL AND CONSOLE I/O ROUTINES, ETC. */ /*
DECLARE BINARY LITERALLY 'ADDRESS', CHARACTER LITERALLY 'BYTE';
DECLARE FIXED LITERALLY ' ', BIT LITERALLY 'BYTE';
DECLARE STATIC LITERALLY ' ', RETURNS LITERALLY ' ';
DECLARE FALSE LITERALLY '0', TRUE LITERALLY '1';
DECLARE HBOUND LITERALLY 'LAST', SADDR LITERALLY '.';
BDOSF: PROCEDURE( FN, ARG )BYTE;
DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
PRCHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END;
PRSTRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
PRNL: PROCEDURE; CALL PRCHAR( 0DH ); CALL PRCHAR( 0AH ); END;
PRNUMBER: PROCEDURE( N );
DECLARE N ADDRESS;
DECLARE V ADDRESS, N$STR( 6 ) BYTE, W BYTE;
N$STR( W := LAST( N$STR ) ) = '$';
N$STR( W := W - 1 ) = '0' + ( ( V := N ) MOD 10 );
DO WHILE( ( V := V / 10 ) > 0 );
N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
END;
CALL BDOS( 9, .N$STR( W ) );
END PRNUMBER;
MODF: PROCEDURE( A, B )ADDRESS;
DECLARE ( A, B )ADDRESS;
RETURN( A MOD B );
END MODF;
/* END LANGUAGE DEFINITIONS */
/* TASK */
DIGITSUM: PROCEDURE( N, BASE )RETURNS /* RETURNS THE DIGIT SUM OF N */ (
FIXED BINARY /* IN THE SPECIFIED BASE */ )
;
DECLARE ( N, BASE ) FIXED BINARY;
DECLARE ( SUM, V ) FIXED BINARY;
SUM = MODF( N, BASE );
V = N / BASE;
DO WHILE( V > 0 );
SUM = SUM + MODF( V, BASE );
V = V / BASE;
END;
RETURN( SUM );
END DIGITSUM ;
ISPRIME: PROCEDURE( N )RETURNS /* RETURNS TRUE IF N IS PRIME, */ (
BIT /* FALSE OTHERWISE */ )
;
DECLARE N FIXED BINARY;
DECLARE I FIXED BINARY;
DECLARE RESULT BIT;
IF N < 2 THEN RESULT = FALSE;
ELSE IF N = 2 THEN RESULT = TRUE;
ELSE IF MODF( N, 2 ) = 0 THEN RESULT = FALSE;
ELSE DO;
RESULT = TRUE;
I = 3;
DO WHILE( RESULT & /*
AND /* */ ( I * I ) <= N );
RESULT = MODF( N, I ) > 0;
I = I + 2;
END;
END;
RETURN( RESULT );
END ISPRIME ;
DECLARE ( I, PCOUNT ) FIXED BINARY;
PCOUNT = 0;
DO I = 1 TO 199;
IF ISPRIME( DIGITSUM( I, 2 ) ) THEN DO;
IF ISPRIME( DIGITSUM( I, 3 ) ) THEN DO;
CALL PRCHAR( ' ' );
IF I < 10 THEN CALL PRCHAR( ' ' );
IF I < 100 THEN CALL PRCHAR( ' ' );
CALL PRNUMBER( I );
PCOUNT = PCOUNT + 1;
IF PCOUNT > 9 THEN DO;
PCOUNT = 0;
CALL PRNL;
END;
END;
END;
END;
EOF: end prime_digit_sums_100H;- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
Python
'''Binary and Ternary digit sums both prime'''
# digitSumsPrime :: Int -> [Int] -> Bool
def digitSumsPrime(n):
'''True if the digits of n in each
given base have prime sums.
'''
def go(bases):
return all(
isPrime(digitSum(b)(n))
for b in bases
)
return go
# digitSum :: Int -> Int -> Int
def digitSum(base):
'''The sum of the digits of n in a given base.
'''
def go(n):
q, r = divmod(n, base)
return go(q) + r if n else 0
return go
# ------------------------- TEST -------------------------
# main :: IO ()
def main():
'''Matching integers in the range [1..199]'''
xs = [
str(n) for n in range(1, 200)
if digitSumsPrime(n)([2, 3])
]
print(f'{len(xs)} matches in [1..199]\n')
print(table(10)(xs))
# ----------------------- GENERIC ------------------------
# chunksOf :: Int -> [a] -> [[a]]
def chunksOf(n):
'''A series of lists of length n, subdividing the
contents of xs. Where the length of xs is not evenly
divible, the final list will be shorter than n.
'''
def go(xs):
return (
xs[i:n + i] for i in range(0, len(xs), n)
) if 0 < n else None
return go
# isPrime :: Int -> Bool
def isPrime(n):
'''True if n is prime.'''
if n in (2, 3):
return True
if 2 > n or 0 == n % 2:
return False
if 9 > n:
return True
if 0 == n % 3:
return False
def p(x):
return 0 == n % x or 0 == n % (2 + x)
return not any(map(p, range(5, 1 + int(n ** 0.5), 6)))
# table :: Int -> [String] -> String
def table(n):
'''A list of strings formatted as
rows of n (right justified) columns.
'''
def go(xs):
w = len(xs[-1])
return '\n'.join(
' '.join(row) for row in chunksOf(n)([
s.rjust(w, ' ') for s in xs
])
)
return go
# MAIN ---
if __name__ == '__main__':
main()
61 matches in [1..199] 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
Quackery
digitsum is defined at Sum digits of an integer#Quackery.
isprime is defined at Primality by trial division#Quackery.
[]
200 times
[ i^ 3 digitsum isprime while
i^ 2 digitsum isprime while
i^ join ]
echo- Output:
[ 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 ]
Raku
say (^200).grep(-> $n {all (2,3).map({$n.base($_).comb.sum.is-prime}) }).batch(10)».fmt('%3d').join: "\n";
- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199
REXX
/*REXX program finds and displays integers whose base 2 and base 3 digit sums are prime.*/
parse arg n cols . /*obtain optional argument from the CL.*/
if n=='' | n=="," then n= 200 /*Not specified? Then use the default.*/
if cols=='' | cols=="," then cols= 10 /* " " " " " " */
call genP /*build array of semaphores for primes.*/
w= 10 /*width of a number in any column. */
title= ' positive integers whose binary and ternary digit sums are prime, N < ' commas(n)
if cols>0 then say ' index │'center(title, 1 + cols*(w+1) ) /*maybe show title.*/
if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─') /*maybe show sep. */
found= 0; idx= 1 /*initialize # of finds and the index. */
$= /*a list of numbers found (so far). */
do j=1 for n-1 /*find #s whose B2 & B3 sums are prime.*/
b2= sumDig( tBase(j, 2) ); if \!.b2 then iterate /*convert to base2, sum digits.*/ /* ◄■■■■■■■■ a filter. */
b3= sumDig( tBase(j, 3) ); if \!.b3 then iterate /* " " base3 " " */ /* ◄■■■■■■■■ a filter. */
found= found + 1 /*bump the number of found integers. */
if cols<1 then iterate /*Only showing the summary? Then skip.*/
$= $ right( commas(j), w) /*add a commatized integer ───► $ list.*/
if found//cols\==0 then iterate /*have we populated a line of output? */
say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */
idx= idx + cols /*bump the index count for the output*/
end /*j*/
if $\=='' then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/
if cols>0 then say '───────┴'center("" , 1 + cols*(w+1), '─') /*show foot sep ? */
say
say 'Found ' commas(found) title /*show summary. */
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
sumDig: procedure; parse arg x 1 s 2;do j=2 for length(x)-1;s=s+substr(x,j,1);end;return s
/*──────────────────────────────────────────────────────────────────────────────────────*/
genP: @= 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103
!.=0; do p=1 for words(@); _= word(@, p); !._= 1; end; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
tBase: procedure; parse arg x,toBase; y=; $= 0123456789
do while x>=toBase; y= substr($, x//toBase+1, 1)y; x= x % toBase
end /*while*/
return substr($, x+1, 1)y
- output when using the default inputs:
index │ positive integers whose binary and ternary digit sums are prime, N < 200 ───────┼─────────────────────────────────────────────────────────────────────────────────────────────────────────────── 1 │ 5 6 7 10 11 12 13 17 18 19 11 │ 21 25 28 31 33 35 36 37 41 47 21 │ 49 55 59 61 65 67 69 73 79 82 31 │ 84 87 91 93 97 103 107 109 115 117 41 │ 121 127 129 131 133 137 143 145 151 155 51 │ 157 162 167 171 173 179 181 185 191 193 61 │ 199 ───────┴─────────────────────────────────────────────────────────────────────────────────────────────────────────────── Found 61 positive integers whose binary and ternary digit sums are prime, N < 200
Ring
load "stdlib.ring"
see "working..." + nl
see "Numbers < 200 whose binary and ternary digit sums are prime:" + nl
decList = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
baseList = ["0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F"]
num = 0
limit = 200
for n = 1 to limit
strBin = decimaltobase(n,2)
strTer = decimaltobase(n,3)
sumBin = 0
for m = 1 to len(strBin)
sumBin = sumBin + number(strBin[m])
next
sumTer = 0
for m = 1 to len(strTer)
sumTer = sumTer + number(strTer[m])
next
if isprime(sumBin) and isprime(sumTer)
num = num + 1
see "" + num + ". {" + n + "," + strBin + ":" + sumBin + "," + strTer + ":" + sumTer + "}" + nl
ok
next
see "Found " + num + " such numbers" + nl
see "done..." + nl
func decimaltobase(nr,base)
binList = []
binary = 0
remainder = 1
while(nr != 0)
remainder = nr % base
ind = find(decList,remainder)
rem = baseList[ind]
add(binList,rem)
nr = floor(nr/base)
end
binlist = reverse(binList)
binList = list2str(binList)
binList = substr(binList,nl,"")
return binList- Output:
working...
Numbers < 200 whose binary and ternary digit sums are prime:
1. {5,101:2,12:3}
2. {6,110:2,20:2}
3. {7,111:3,21:3}
4. {10,1010:2,101:2}
5. {11,1011:3,102:3}
6. {12,1100:2,110:2}
7. {13,1101:3,111:3}
8. {17,10001:2,122:5}
9. {18,10010:2,200:2}
10. {19,10011:3,201:3}
11. {21,10101:3,210:3}
12. {25,11001:3,221:5}
13. {28,11100:3,1001:2}
14. {31,11111:5,1011:3}
15. {33,100001:2,1020:3}
16. {35,100011:3,1022:5}
17. {36,100100:2,1100:2}
18. {37,100101:3,1101:3}
19. {41,101001:3,1112:5}
20. {47,101111:5,1202:5}
21. {49,110001:3,1211:5}
22. {55,110111:5,2001:3}
23. {59,111011:5,2012:5}
24. {61,111101:5,2021:5}
25. {65,1000001:2,2102:5}
26. {67,1000011:3,2111:5}
27. {69,1000101:3,2120:5}
28. {73,1001001:3,2201:5}
29. {79,1001111:5,2221:7}
30. {82,1010010:3,10001:2}
31. {84,1010100:3,10010:2}
32. {87,1010111:5,10020:3}
33. {91,1011011:5,10101:3}
34. {93,1011101:5,10110:3}
35. {97,1100001:3,10121:5}
36. {103,1100111:5,10211:5}
37. {107,1101011:5,10222:7}
38. {109,1101101:5,11001:3}
39. {115,1110011:5,11021:5}
40. {117,1110101:5,11100:3}
41. {121,1111001:5,11111:5}
42. {127,1111111:7,11201:5}
43. {129,10000001:2,11210:5}
44. {131,10000011:3,11212:7}
45. {133,10000101:3,11221:7}
46. {137,10001001:3,12002:5}
47. {143,10001111:5,12022:7}
48. {145,10010001:3,12101:5}
49. {151,10010111:5,12121:7}
50. {155,10011011:5,12202:7}
51. {157,10011101:5,12211:7}
52. {162,10100010:3,20000:2}
53. {167,10100111:5,20012:5}
54. {171,10101011:5,20100:3}
55. {173,10101101:5,20102:5}
56. {179,10110011:5,20122:7}
57. {181,10110101:5,20201:5}
58. {185,10111001:5,20212:7}
59. {191,10111111:7,21002:5}
60. {193,11000001:3,21011:5}
61. {199,11000111:5,21101:5}
Found 61 such numbers
done...
RPL
« → base
« 0 SWAP
WHILE DUP NOT REPEAT
base MOD LASTARG / IP
UNROT + SWAP
END
DROP
» » 'BDSUM' STO
« { }
1 200 FOR j
IF j 3 BDSUM ISPRIME? THEN
IF j 2 BDSUM ISPRIME THEN
j +
END END
NEXT
» 'TASK' STO
- Output:
1: { 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 14 5 151 155 157 162 167 171 173 179 181 185 191 193 199 }
Ruby
require 'prime'
p (1..200).select{|n| [2, 3].all?{|base| n.digits(base).sum.prime?} }
- Output:
[5, 6, 7, 10, 11, 12, 13, 17, 18, 19, 21, 25, 28, 31, 33, 35, 36, 37, 41, 47, 49, 55, 59, 61, 65, 67, 69, 73, 79, 82, 84, 87, 91, 93, 97, 103, 107, 109, 115, 117, 121, 127, 129, 131, 133, 137, 143, 145, 151, 155, 157, 162, 167, 171, 173, 179, 181, 185, 191, 193, 199]
Sidef
1..^200 -> grep {|n| [2,3].all { n.sumdigits(_).is_prime } }
- Output:
[5, 6, 7, 10, 11, 12, 13, 17, 18, 19, 21, 25, 28, 31, 33, 35, 36, 37, 41, 47, 49, 55, 59, 61, 65, 67, 69, 73, 79, 82, 84, 87, 91, 93, 97, 103, 107, 109, 115, 117, 121, 127, 129, 131, 133, 137, 143, 145, 151, 155, 157, 162, 167, 171, 173, 179, 181, 185, 191, 193, 199]
Wren
import "./math" for Int
import "./fmt" for Fmt
var numbers = []
for (i in 2..199) {
var bds = Int.digitSum(i, 2)
if (Int.isPrime(bds)) {
var tds = Int.digitSum(i, 3)
if (Int.isPrime(tds)) numbers.add(i)
}
}
System.print("Numbers < 200 whose binary and ternary digit sums are prime:")
Fmt.tprint("$4d", numbers, 14)
System.print("\nFound %(numbers.count) such numbers.")
- Output:
Numbers < 200 whose binary and ternary digit sums are prime: 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 Found 61 such numbers.
XPL0
func IsPrime(N); \Return 'true' if N is a prime number
int N, I;
[if N <= 1 then return false;
for I:= 2 to sqrt(N) do
if rem(N/I) = 0 then return false;
return true;
];
func SumDigits(N, Base); \Return sum of digits in N for Base
int N, Base, Sum;
[Sum:= 0;
repeat N:= N/Base;
Sum:= Sum + rem(0);
until N=0;
return Sum;
];
int Count, N;
[Count:= 0;
for N:= 0 to 200-1 do
if IsPrime(SumDigits(N,2)) & IsPrime(SumDigits(N,3)) then
[IntOut(0, N);
Count:= Count+1;
if rem(Count/10) = 0 then CrLf(0) else ChOut(0, 9\tab\);
];
CrLf(0);
IntOut(0, Count);
Text(0, " such numbers found below 200.
");
]- Output:
5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 61 such numbers found below 200.