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A256876 Numbers divisible by prime(d) for each digit d in their base-6 representation, none of which may be zero.

%I A256876 #17 Apr 05 2024 00:38:29
%S A256876 15,28,154,280,525,555,735,910,1036,1078,1666,3795,4270,4665,4690,
%T A256876 5446,5530,5572,5775,5950,6202,7755,9352,9982,10108,13888,14014,15400,
%U A256876 18705,18885,18915,19965,19995,20175,20475,20625,21735,21945,22605,26445,26475,26565,26655,27735,27995,28000,28035
%N A256876 Numbers divisible by prime(d) for each digit d in their base-6 representation, none of which may be zero.
%C A256876 Base-6 analog of A256786. See A256874 - A256879 for the base-4, ..., base-9 analogs.
%C A256876 See A256866 for a variant where divisibility by prime(d+1) is required instead.
%C A256876 Since digit 0 is not allowed, no terms are divisible by 6, so digits 1 and 2 can't both be present. - _Robert Israel_, Apr 04 2024
%H A256876 Robert Israel, <a href="/A256876/b256876.txt">Table of n, a(n) for n = 1..10000</a>
%p A256876 P:= [2,3,5,7,11]:
%p A256876 filter6:= proc(n) local S,s;
%p A256876   S:= convert(convert(n,base,6),set);
%p A256876   if member(0,S) then return false fi;
%p A256876   n mod mul(P[s],s=S) = 0
%p A256876 end proc:
%p A256876 S1:= {1}; S2:= {2}; S0:= {3,4,5}: R:= select(filter6, S0 union S1 union S2):
%p A256876 for i from 2 to 10 do
%p A256876   S1:= map(t -> (6*t+1, 6*t+3,6*t+4, 6*t+5), S1) union map(t -> 6*t+1, S0);
%p A256876   S2:= map(t -> (6*t+2, 6*t+3, 6*t+4, 6*t+5), S2) union map(t -> 6*t+2, S0);
%p A256876   S0:= map(t -> (6*t+3,6*t+4,6*t+5), S0);
%p A256876   R:= R union select(filter6, S0) union select(filter6, S1) union select(filter6, S2);
%p A256876 od:
%p A256876 sort(convert(R,list)); # _Robert Israel_, Apr 04 2024
%t A256876 ndpQ[n_]:=Module[{ds=Union[IntegerDigits[n,6]]},FreeQ[ds,0]&&And@@ Table[ Divisible[n,Prime[i]],{i,ds}]]; Select[Range[20000],ndpQ] (* _Harvey P. Dale_, May 29 2015 *)
%o A256876 (PARI) is(n,b=6)=!for(i=1,#d=Set(digits(n,b)),(!d[i]||n%prime(d[i]))&&return)
%Y A256876 Cf. A256786, A256874 - A256879, A256868, A256882 - A256884, A256865 - A256870.
%K A256876 nonn,base
%O A256876 1,1
%A A256876 _M. F. Hasler_, Apr 11 2015
%E A256876 More terms from _Robert Israel_, Apr 04 2024