Show the (decimal) value of a number of 1s appended with a 3, then squared: Difference between revisions
Show the (decimal) value of a number of 1s appended with a 3, then squared (view source)
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;Task:
Show here (on this page) the decimal numbers formed by:
:: <big><big>(</big></big>'''n''' '''1''''s appended by the digit '''3'''<big><big>)</big></big> and then square the result, where <big> '''0 <= n < 8''' </big>
;See also
;* [[oeis:A151997]]
=={{header|11l}}==
{{trans|Python}}
<syntaxhighlight lang="11l">L(i) 0..7 {print(‘( ’(‘1’ * i)‘3 ) ^ 2 = ’(Int64((‘1’ * i)‘3’) ^ 2))}</syntaxhighlight>
Line 89 ⟶ 91:
INT pos := 0;
STRING pattern := "123456790";
INT p len := ( UPB pattern - LWB pattern ) + 1;
WHILE string in string( pattern, pos, v ) DO
v := v[ 1 : pos - 1 ] + "A" + v[ pos + p len : ]
Line 135 ⟶ 137:
111 AAAAAAAAAAAA12387654320ZZZZZZZZZZZ98769
</pre>
=={{header|Arturo}}==
<syntaxhighlight lang="rebol">loop 0..7 'x [
num: to :integer(repeat "1" x) ++ "3"
Line 143 ⟶ 145:
{{out}}
<pre>3 9
13 169
Line 202 ⟶ 203:
-> 123456832098769
</pre>
=={{header|BQN}}==
<syntaxhighlight lang="bqn">≍˘⟜(ט) 2(¯17+×)` 8⥊10</syntaxhighlight>
{{out}}
<pre>┌─
╵ 3 9
13 169
113 12769
1113 1238769
11113 123498769
111113 12346098769
1111113 1234572098769
11111113 123456832098769
┘</pre>
=={{header|C}}==
Line 357 ⟶ 372:
11111113
-> 123456832098769
</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
procedure OnesPlusThree(Memo: TMemo);
{Create pattern: 3, 13, 113, 1113, and square}
var NS: string;
var I: integer;
var NV: int64;
begin
{Start with 3 in number string}
NS:='3';
for I:=1 to 7 do
begin
{Convert to a number}
NV:=StrToInt(NS);
Memo.Lines.Add(Format('%2D - %10d^2 =%18.0n',[I,NV,NV*NV+0.0]));
{Add a "1" to the number string}
NS:='1'+NS;
end;
end;
</syntaxhighlight>
{{out}}
<pre>
1 - 3^2 = 9
2 - 13^2 = 169
3 - 113^2 = 12,769
4 - 1113^2 = 1,238,769
5 - 11113^2 = 123,498,769
6 - 111113^2 = 12,346,098,769
7 - 1111113^2 = 1,234,572,098,769
Elapsed Time: 8.668 ms.
</pre>
Line 409 ⟶ 460:
1111113 1234572098769
11111113 123456832098769
</pre>
Line 451 ⟶ 474:
: show dup . ." ^2 = " sqr . cr ;
: show-upto
0 swap
begin over over < while
Line 463 ⟶ 486:
{{out}}
<pre>3 ^2 = 9
13 ^2 = 169
Line 472 ⟶ 494:
1111113 ^2 = 1234572098769
11111113 ^2 = 123456832098769</pre>
=={{header|FreeBASIC}}==
<syntaxhighlight lang="freebasic">function make13(n as uinteger) as uinteger
dim as uinteger t = 0
while n
t = 10*(t+1)
n-=1
wend
return t+3
end function
dim as ulongint m
for n as uinteger = 0 to 7
m = make13(n)^2
print make13(n), m
next n</syntaxhighlight>
{{out}}
<pre>
3 9
13 169
113 12769
1113 1238769
11113 123498769
111113 12346098769
1111113 1234572098769
11111113 123456832098769
</pre>
=={{header|Go}}==
Line 523 ⟶ 573:
format <$> onesPlusThree</syntaxhighlight>
{{out}}
<pre> 3^2 = 9
13^2 = 169
Line 534 ⟶ 583:
=={{header|J}}==
<syntaxhighlight lang="j"> (,. *:) (9 %~ 17 + 10x ^ >:) i. 8
3 9
13 169
Line 543 ⟶ 591:
111113 12346098769
1111113 1234572098769
11111113 123456832098769</syntaxhighlight>
=={{header|JavaScript}}==
<syntaxhighlight lang="javascript">
'use strict'
let n = 0
for( let i = 1; i < 8; i ++ )
{
let n3 = ( n * 10 ) + 3
console.log( n3 + " " + ( n3 * n3 ) )
n *= 10
n += 1
}
</syntaxhighlight>
{{out}}
<pre>
3 9
13 169
113 12769
1113 1238769
11113 123498769
111113 12346098769
1111113 1234572098769
</pre>
=={{header|jq}}==
Line 576 ⟶ 646:
'''For 100 <= n <= 105'''
Encoding "123456790" as "A", "987654320" as Z", and lastly "9876" as "N":
<syntaxhighlight lang="jq">range(100; 106) as $n
| ((("1"*$n) + "3") | tonumber) as $number
Line 609 ⟶ 679:
7 11111113 123456832098769
</pre>
=={{header|K}}==
<syntaxhighlight lang="k">{x,'x*x}2(-17+*)\8#10</syntaxhighlight>
{{out}}
<pre>(3 9
13 169
113 12769
1113 1238769
11113 123498769
111113 12346098769
1111113 1234572098769
11111113 123456832098769)</pre>
=={{header|Lua}}==
<syntaxhighlight lang="lua">
do
local n = 0
for i = 1,8 do
local n3 = ( n * 10 ) + 3
io.write( n3, " ", n3 * n3, "\n" )
n = ( n * 10 ) + 1
end
end</syntaxhighlight>
{{out}}
<pre>
3 9
13 169
113 12769
1113 1238769
11113 123498769
111113 12346098769
1111113 1234572098769
11111113 123456832098769
</pre>
=={{header|MAD}}==
<syntaxhighlight lang="mad"> NORMAL MODE IS INTEGER
Line 629 ⟶ 734:
11111113**2 = 123456832098769</pre>
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">{#, #^2} & /@
Table[FromDigits[PadLeft[{3}, n, 1]], {n, 9}] // TableForm</syntaxhighlight>
Line 685 ⟶ 790:
1111113 1234572098769
11111113 123456832098769</pre>
=={{header|PARI/GP}}==
<syntaxhighlight lang="parigp">Make13(n)=m=0;while(n>0,m=10*(m+1);n=n-1);m=3+m;return(m)
for(i=0,7,print(Make13(i)," ",Make13(i)^2))</syntaxhighlight>
{{out}}
<pre>3 9
13 169
113 12769
1113 1238769
11113 123498769
111113 12346098769
1111113 1234572098769
11111113 123456832098769
</pre>
=={{header|Pascal}}==
==={{header|Free Pascal}}===
like [[Show_the_(decimal)_value_of_a_number_of_1s_appended_with_a_3,_then_squared#Phix|Phix]] using byte, and convert than to ASCII.
Because the values are calculated one by one, one can use addition to get rid of calculating squares, by using binomial formula.
The best is shown in [[Show_the_(decimal)_value_of_a_number_of_1s_appended_with_a_3,_then_squared#ALGOL_68|Algol_68]] that it ends in a cyclic pattern of lenght 9.
<syntaxhighlight lang="pascal">{
10^pot+k -> prepend a 1 1113-> 11113
(10^pot+k)^2 = 10^(2*pot)+ 2*10^pot*k + k^2
(10^pot+k)^2 = 10^pot*(10^pot+2*k) + k^2
s_lastsqr = k*k
s_DeltaSqr = (10^pot+2*k) => 1222....2226
shift s_DeltaSqr by pot digits in SumMyDeltaSqr => 10^pot*(10^pot+2*k)
}
program OnesAppend3AndSquare;
const
MAX = 3700;
type
tmyNumb = array of byte;
var
res :AnsiString;
procedure OutMyNumb(const n: tmyNUmb;l,w: integer);
var
i,ofs : integer;
begin
l += 1;
if w < l then
w := l+1;
setlength(res,w);
fillchar(res[1],w,' ');
ofs := w-l;
For i := 1 to l do
res[i+ofs] := chr(n[l-i]+48);
write(res);
end;
procedure Out_k_sqr(const k,sqr_k: tmyNUmb;pot:integer);
var
dgtcnt : integer;
Begin
write(pot:4);
dgtcnt := 22;
if pot > 10 then
dgtcnt := 78;
OutMyNumb(k,pot,dgtcnt-4);
if pot > 10 then
writeln;
OutMyNumb(sqr_k,2*pot,dgtcnt);
writeln;
end;
procedure SumMyDeltaSqr(var res:tmyNUmb;const s:tmyNumb;pot: integer);
//res = s_lastsqr
//s = s_DeltaSqr
//shift s by l => (10^pot) * s_DeltaSqr = 10^pot*(10^pot+2*k)
var
i,sum,carry : integer;
begin
carry := 0;
For i := 0 to pot+1 do
begin
sum := res[i+pot]+s[i]+carry;
carry := ord(sum>9);
sum -= (-carry) AND 10;
res[i+pot] := sum;
end;
end;
var
s,s_DeltaSqr,s_lastsqr : tmyNumb;
pot: integer;
Begin
setlength(s,MAX);
setlength(s_DeltaSqr,Max+1);
setlength(s_lastsqr,2*Max+1);
pot := 0;
s[pot] := 3;
s_lastsqr[pot] := 9;
repeat
SumMyDeltaSqr(s_lastsqr,s_DeltaSqr,pot);
if pot < 10 then
Out_k_sqr(s,s_lastsqr,pot);
if pot = 37 then
Out_k_sqr(s,s_lastsqr,pot);
if pot > 0 then
s_DeltaSqr[pot]:= 2 // =>2*s[i] 2222...26
else
s_DeltaSqr[0] := 6;// =>2*s[0] 6
inc(pot);
s_DeltaSqr[pot]:= 1; //1...6
s[pot] := 1;
until pot = MAX;
Writeln('Finished til ',MAX);
end.
</syntaxhighlight>
{{out|@TIO.RUN}}
<pre>
0 3 9
1 13 169
2 113 12769
3 1113 1238769
4 11113 123498769
5 111113 12346098769
6 1111113 1234572098769
7 11111113 123456832098769
8 111111113 12345679432098769
9 1111111113 1234567905432098769
37 11111111111111111111111111111111111113
123456790123456790123456790123456790165432098765432098765432098765432098769
Finished til 3700
Real time: 0.106 s CPU share: 99.03 %
@home real 0m0.016s
</pre>
=={{header|Perl}}==
<syntaxhighlight lang="perl">#!/usr/bin/perl
use strict; # https://rosettacode.org/wiki/Show_the_(decimal)_value_of_a_number_of_1s_appended_with_a_3,_then_squared
use warnings;
#use bignum; # uncomment for larger than 9 or 32-bit perls
for ( 0 .. 7 )
{
my $number = 1 x $_ . 3;
print "$number ", $number ** 2, "\n";
}</syntaxhighlight>
{{out}}
<pre>
3 9
13 169
113 12769
1113 1238769
11113 123498769
111113 12346098769
1111113 1234572098769
11111113 123456832098769
</pre>
=={{header|Phix}}==
Perfect opportunity for a little string math, why not...
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">37</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'3'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)&</span><span style="color: #008000;">'9'</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"0"</span> <span style="color: #0000FF;">&</span> <span style="color: #000000;">res</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">digit</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">3</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">i</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">digit</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]-</span><span style="color: #008000;">'0'</span>
<span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digit</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)+</span><span style="color: #008000;">'0'</span>
<span style="color: #000000;">digit</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">digit</span><span style="color: #0000FF;">/</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%38s %75s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'1'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)&</span><span style="color: #008000;">'3'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
3 9
13 169
113 12769
1113 1238769
11113 123498769
111113 12346098769
1111113 1234572098769
11111113 123456832098769
111111113 12345679432098769
1111111113 1234567905432098769
11111111113 123456790165432098769
111111111113 12345679012765432098769
1111111111113 1234567901238765432098769
11111111111113 123456790123498765432098769
111111111111113 12345679012346098765432098769
1111111111111113 1234567901234572098765432098769
11111111111111113 123456790123456832098765432098769
111111111111111113 12345679012345679432098765432098769
1111111111111111113 1234567901234567905432098765432098769
11111111111111111113 123456790123456790165432098765432098769
111111111111111111113 12345679012345679012765432098765432098769
1111111111111111111113 1234567901234567901238765432098765432098769
11111111111111111111113 123456790123456790123498765432098765432098769
111111111111111111111113 12345679012345679012346098765432098765432098769
1111111111111111111111113 1234567901234567901234572098765432098765432098769
11111111111111111111111113 123456790123456790123456832098765432098765432098769
111111111111111111111111113 12345679012345679012345679432098765432098765432098769
1111111111111111111111111113 1234567901234567901234567905432098765432098765432098769
11111111111111111111111111113 123456790123456790123456790165432098765432098765432098769
111111111111111111111111111113 12345679012345679012345679012765432098765432098765432098769
1111111111111111111111111111113 1234567901234567901234567901238765432098765432098765432098769
11111111111111111111111111111113 123456790123456790123456790123498765432098765432098765432098769
111111111111111111111111111111113 12345679012345679012345679012346098765432098765432098765432098769
1111111111111111111111111111111113 1234567901234567901234567901234572098765432098765432098765432098769
11111111111111111111111111111111113 123456790123456790123456790123456832098765432098765432098765432098769
111111111111111111111111111111111113 12345679012345679012345679012345679432098765432098765432098765432098769
1111111111111111111111111111111111113 1234567901234567901234567901234567905432098765432098765432098765432098769
11111111111111111111111111111111111113 123456790123456790123456790123456790165432098765432098765432098765432098769
</pre>
=={{header|Plain English}}==
Line 716 ⟶ 1,032:
=={{header|Python}}==
===One Liner===
The most Pythonic way
<syntaxhighlight lang="python">
[print("( " + "1"*i + "3 ) ^ 2 = " + str(int("1"*i + "3")**2)) for i in range(0,8)]
Line 731 ⟶ 1,047:
( 11111113 ) ^ 2 = 123456832098769
</pre>
===Procedural===
<syntaxhighlight lang="python">#!/usr/bin/python
def make13(n):
return 10 ** (n + 1) // 9 + 2
for n in
print('%9d%16d' % (n, n * n))</syntaxhighlight>
===Functional===
Taking the first n terms from an infinite series:
<syntaxhighlight lang="python">'''Sequence of 1s appended with a 3, then squared'''
Line 846 ⟶ 1,156:
=={{header|Quackery}}==
<syntaxhighlight lang="quackery"> [ char 1 swap of
char 3 join
$->n drop ] is 1's+3 ( n -> n )
8 times
[ i^ 1's+3
dup echo
say " --> "
dup * echo cr ]</syntaxhighlight>
{{out}}
<pre>3 --> 9
13 --> 169
Line 867 ⟶ 1,175:
1111113 --> 1234572098769
11111113 --> 123456832098769</pre>
=={{header|Raku}}==
In an attempt to stave of terminal ennui, Find the first 8 where a(n) is semiprime.
<syntaxhighlight lang="raku" line>say "$_, {.²}" for (^∞).map({ ( 1 x $_ ~ 3)} ).grep({ .is-prime })[^8]</syntaxhighlight>
{{out}}
Line 1,153 ⟶ 1,263:
for n = 1 to limit
if n = 1
strn = number(str)
res = pow(strn,2)
see "{" + strn + "," + res + "}" + nl
else
str = "1" + strn
strn = number(str)
res = pow(strn,2)
see "{" + strn + "," + res + "}" + nl
ok
next
Line 1,178 ⟶ 1,288:
{11111113,123456832098769}
done...
</pre>
=={{header|RPL}}==
{{works with|HP|49}}
≪ { }
0 7 '''FOR''' n
10 n ^ 1 - 9 / 10 * 3 + SQ +
'''NEXT'''
≫ '<span style="color:blue">TASK</span>' STO
{{out}}
<pre>
1: { 9 169 12769 1238769 123498769 12346098769 1234572098769 123456832098769 }
</pre>
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">m = 8
(0..m).each do |n|
ones3 = "1"*n +"3"
puts ones3.ljust(m+2) + ( ones3.to_i**2).to_s
end</syntaxhighlight>
{{out}}
<pre>3 9
13 169
113 12769
1113 1238769
11113 123498769
111113 12346098769
1111113 1234572098769
11111113 123456832098769
111111113 12345679432098769
</pre>
Line 1,259 ⟶ 1,399:
=={{header|Wren}}==
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
var a = Fn.new { |n|
| |||