A127937 Length of longest string of consecutive zeros in the base-7 expansion of 2^n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 0, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1

Offset

0,39

Comments

Is a(n) >= 3 for all n >= 8834?

Links

Table of n, a(n) for n=0..104.

Example

a(42)=2 because the base-7 expansion of 2^42 is 113200616214553321.

Prog

#!/usr/bin/perl -l $|++; use Math::GMP; use strict; my $n = new Math::GMP 1; my $pow = 0; while (1) { my $base7 = basebexpansionofn(7, $n); my $maxconsecutivezeros = 0; while ($base7 =~ /(0+)/g) { if (length($1) > $maxconsecutivezeros) { $maxconsecutivezeros = length($1); } } print "a($pow)=$maxconsecutivezeros"; $n *= 2; $pow++; } sub basebexpansionofn { my ($b, $n) = @_; return '0' if $n == 0; my $lastdigit = $n % $b; my $firstdigits = ($n - $lastdigit)/$b; return ($firstdigits ? basebexpansionofn($b, $firstdigits) : '').$lastdigit; }

Crossrefs

Sequence in context: A082586 A160094 A043283 * A250209 A280010 A167852

Adjacent sequences: A127934 A127935 A127936 * A127938 A127939 A127940

Keyword

nonn

Author

Josh Purinton (joshpurinton(AT)gmail.com), Apr 06 2007

Status

approved