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

1,2

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

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 *)

Crossrefs

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

Sequence in context: A321372 A001948 A121912 * A328393 A189529 A120514

Adjacent sequences: A325110 A325111 A325112 * A325114 A325115 A325116

Keyword

nonn,base

Author

Jonathan Kal-El Peréz, Mar 27 2019

Extensions

Corrected by Robert Israel, Apr 14 2020

Status

approved