A325113 - OEIS

%I #26 Apr 14 2020 19:58:32

%S 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,

%T 39,50,51,53,55,57,59,61,62,63,65,66,67,69,70,71,73,75,77,79,90,91,93,

%U 95,97,99,101,103,105,107,109,110,111,113,115,117

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

%C From _Robert Israel_, Apr 14 2020: (Start)

%C There are no digits 4 or 8.

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

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

%H Robert Israel, <a href="/A325113/b325113.txt">Table of n, a(n) for n = 1..10000</a>

%p filter:= proc(n) local L,i;

%p   L:= convert(n,base,10);

%p   if member(4,L) or member(8,L) then return false fi;

%p   if member(0,L,i) and hastype(L[i+1..-1],even) then return false fi;

%p   i:= ListTools:-SelectFirst(t -> t=2 or t=6, L,output=indices);

%p   i = NULL or not hastype(L[i+1..-1],odd);

%p end proc:

%p select(filter, [$1..300]); # _Robert Israel_, Apr 14 2020

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

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

%K nonn,base

%O 1,2

%A _Jonathan Kal-El Peréz_, Mar 27 2019

%E Corrected by _Robert Israel_, Apr 14 2020