A325113 Positive integers whose decimal representation has no nonzero subsequence that is divisible by 4.

1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 15, 17, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 35, 37, 39, 50, 51, 53, 55, 57, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 75, 77, 79, 90, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 110, 111, 113, 115, 117

Offset: 1

Author

Jonathan Kal-El Peréz, Mar 27 2019

Keywords

• nonn
• base

Comments

From Robert Israel, Apr 14 2020: (Start)

There are no digits 4 or 8.

If there is a digit 2 or 6, all previous digits must be even.

If there is a digit 0, all previous digits must be odd. (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014261 (for 2), A325112 (for 3), A261189 (for 5).

Programs

Maple

filter:= proc(n) local L,i;
  L:= convert(n,base,10);
  if member(4,L) or member(8,L) then return false fi;
  if member(0,L,i) and hastype(L[i+1..-1],even) then return false fi;
  i:= ListTools:-SelectFirst(t -> t=2 or t=6, L,output=indices);
  i = NULL or not hastype(L[i+1..-1],odd);
end proc:
select(filter, [$1..300]); # Robert Israel, Apr 14 2020

Mathematica

With[{k = 4}, Select[Range@ 120, NoneTrue[DeleteCases[FromDigits /@ Rest@ Subsequences[IntegerDigits@ #], 0], Mod[#, k] == 0 &] &]] (* Michael De Vlieger, Mar 31 2019 *)

Extensions

Corrected by Robert Israel, Apr 14 2020