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Numbers divisible by prime(d) for each digit d in their base-6 representation, none of which may be zero.
2

%I #17 Apr 05 2024 00:38:29

%S 15,28,154,280,525,555,735,910,1036,1078,1666,3795,4270,4665,4690,

%T 5446,5530,5572,5775,5950,6202,7755,9352,9982,10108,13888,14014,15400,

%U 18705,18885,18915,19965,19995,20175,20475,20625,21735,21945,22605,26445,26475,26565,26655,27735,27995,28000,28035

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

%C Base-6 analog of A256786. See A256874 - A256879 for the base-4, ..., base-9 analogs.

%C See A256866 for a variant where divisibility by prime(d+1) is required instead.

%C 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 Robert Israel, <a href="/A256876/b256876.txt">Table of n, a(n) for n = 1..10000</a>

%p P:= [2,3,5,7,11]:

%p filter6:= proc(n) local S,s;

%p S:= convert(convert(n,base,6),set);

%p if member(0,S) then return false fi;

%p n mod mul(P[s],s=S) = 0

%p end proc:

%p S1:= {1}; S2:= {2}; S0:= {3,4,5}: R:= select(filter6, S0 union S1 union S2):

%p for i from 2 to 10 do

%p S1:= map(t -> (6*t+1, 6*t+3,6*t+4, 6*t+5), S1) union map(t -> 6*t+1, S0);

%p S2:= map(t -> (6*t+2, 6*t+3, 6*t+4, 6*t+5), S2) union map(t -> 6*t+2, S0);

%p S0:= map(t -> (6*t+3,6*t+4,6*t+5), S0);

%p R:= R union select(filter6, S0) union select(filter6, S1) union select(filter6, S2);

%p od:

%p sort(convert(R,list)); # _Robert Israel_, Apr 04 2024

%t 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 (PARI) is(n,b=6)=!for(i=1,#d=Set(digits(n,b)),(!d[i]||n%prime(d[i]))&&return)

%Y Cf. A256786, A256874 - A256879, A256868, A256882 - A256884, A256865 - A256870.

%K nonn,base

%O 1,1

%A _M. F. Hasler_, Apr 11 2015

%E More terms from _Robert Israel_, Apr 04 2024