A050607 Numbers k such that base 5 expansion matches (0|1|2)*((0|1)(3|4))?(0|1|2)*.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 20, 21, 22, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 40, 41, 42, 45, 46, 47, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 75, 76, 77, 80, 81, 82, 85, 86, 87, 100, 101, 102, 105, 106, 107, 110, 111, 112, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 140, 141, 142, 145

Offset: 1

Author

Antti Karttunen, Oct 24 1999

Keywords

• nonn
• easy
• base

Comments

25 does not divide C(2s-1,s) = A001700(s) (nor C(2s,s) = A000984(s), central column of Pascal's triangle) if and only if s is one of the terms in this sequence.

Links

• Index entries for 5-automatic sequences.

Crossrefs

Cf. A037453, A046097, A050608, A051382.

Programs

Perl

sub conv_x_base_n { my($x,$b) = @_; my ($r,$z) = (0,'');
do { $r = $x % $b; $x = ($x - $r)/$b; $z = "$r" . $z; } while(0 != $x);
return($z); }
for($i=0; $i <= 201; $i++) { if(("0" . conv_x_base_n($i,5)) =~ /^(0|1|2)*((0|1)(3|4))?(0|1|2)*$/) { print $i, ","; } }

Extensions

a(1)=0 inserted by Georg Fischer, Jun 26 2021