First power of 2 that has leading decimal digits of 12: Difference between revisions

}</lang>

{{out}}

<pre>p(12, 1): 1st power of two (2^n) that starts with '12' is at n = 7

p(12, 2): 2nd power of two (2^n) that starts with '12' is at n = 80

p(123, 45): 45th power of two (2^n) that starts with '123' is at n = 12,710

p(123, 12345): 12,345th power of two (2^n) that starts with '123' is at n = 3,510,491

p(123, 678910): 678,910th power of two (2^n) that starts with '123' is at n = 193,060,223</pre>

=={{header|Perl 6}}==

{{works with|Rakudo|2019.11}}

Uses logs similar to Go and Pascal entries. Takes advantage of patterns in the powers to cut out a bunch of calculations.

<lang perl6>use Lingua::EN::Numbers;

constant $ln2ln10 = log(2) / log(10);

my @startswith12 = ^∞ .grep: { ( 10 ** ($_ * $ln2ln10 % 1) ).substr(0,3) eq '1.2' };

my @startswith123 = lazy gather loop {

state $pre = '1.23';

state $count = 0;

state $this = 0;

given $this {

when 196 {

$this = 289;

my \n = $count + $this;

$this = 485 unless ( 10 ** (n * $ln2ln10 % 1) ).substr(0,4) eq $pre;

}

when 485 {

$this = 196;

my \n = $count + $this;

$this = 485 unless ( 10 ** (n * $ln2ln10 % 1) ).substr(0,4) eq $pre;

}

when 289 { $this = 196 }

when 90 { $this = 289 }

when 0 { $this = 90 }

}

take $count += $this;

}

multi p ($prefix where *.chars == 2, $nth) { @startswith12[$nth-1] }

multi p ($prefix where *.chars == 3, $nth) { @startswith123[$nth-1] }

# The Task

for < 12 1 12 2 123 45 123 12345 123 678910 > -> $prefix, $nth {

printf "%-15s %9s power of two (2^n) that starts with %5s is at n = %s\n", "p($prefix, $nth):",

comma($nth) ~ ordinal-digit($nth).substr(*-2), "'$prefix'", comma p($prefix, $nth);