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A256875 Numbers divisible by prime(d) for each digit d in their base-5 representation, none of which may be zero.

%I A256875 #16 Apr 05 2024 00:39:19
%S A256875 6,12,36,156,162,186,282,306,312,546,784,786,906,912,924,936,1246,
%T A256875 1536,1806,2674,2814,2856,3906,3912,3936,4032,4056,4062,4074,4284,
%U A256875 4536,4656,4662,4686,4746,4914,5796,5922,6174,7032,7056,7062,7182,7434,7656,7662,7686,7782,7806,7812,8064,8106,8946,9072,9114,9282,9324
%N A256875 Numbers divisible by prime(d) for each digit d in their base-5 representation, none of which may be zero.
%C A256875 Base-5 analog of A256786. See A256874 - A256879 for the base-3, ..., base-9 analogs.
%C A256875 See A256865 for a variant where divisibility by prime(d+1) is required instead.
%C A256875 From _Robert Israel_, Apr 04 2024: (Start)
%C A256875 Since digit 0 is not allowed, terms can't be divisible by 5, so digit 3 is also not allowed.
%C A256875 All terms are even. (End)
%H A256875 Robert Israel, <a href="/A256875/b256875.txt">Table of n, a(n) for n = 1..10000</a>
%p A256875 P:= [seq(ithprime(i),i=1..4)]:
%p A256875 filter:= proc(n) local S,s;
%p A256875   S:= convert(convert(n,base,5),set);
%p A256875   if member(0,S) then return false fi;
%p A256875   n mod mul(P[s],s=S) = 0
%p A256875 end proc:
%p A256875 select(filter, [$1..10^4]); # _Robert Israel_, Apr 04 2024
%o A256875 (PARI) is(n,b=5)=!for(i=1,#d=Set(digits(n,b)),(!d[i]||n%prime(d[i]))&&return)
%Y A256875 Cf. A256786, A256874 - A256879, A256882 - A256884, A256865 - A256870.
%K A256875 nonn,base
%O A256875 1,1
%A A256875 _M. F. Hasler_, Apr 11 2015