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

15, 28, 154, 280, 525, 555, 735, 910, 1036, 1078, 1666, 3795, 4270, 4665, 4690, 5446, 5530, 5572, 5775, 5950, 6202, 7755, 9352, 9982, 10108, 13888, 14014, 15400, 18705, 18885, 18915, 19965, 19995, 20175, 20475, 20625, 21735, 21945, 22605, 26445, 26475, 26565, 26655, 27735, 27995, 28000, 28035

Offset

1,1

Comments

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

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

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

P:= [2, 3, 5, 7, 11]:
filter6:= proc(n) local S, s;
  S:= convert(convert(n, base, 6), set);
  if member(0, S) then return false fi;
  n mod mul(P[s], s=S) = 0
end proc:
S1:= {1}; S2:= {2}; S0:= {3, 4, 5}: R:= select(filter6, S0 union S1 union S2):
for i from 2 to 10 do
  S1:= map(t -> (6*t+1, 6*t+3, 6*t+4, 6*t+5), S1) union map(t -> 6*t+1, S0);
  S2:= map(t -> (6*t+2, 6*t+3, 6*t+4, 6*t+5), S2) union map(t -> 6*t+2, S0);
  S0:= map(t -> (6*t+3, 6*t+4, 6*t+5), S0);
  R:= R union select(filter6, S0) union select(filter6, S1) union select(filter6, S2);
od:
sort(convert(R, list)); # Robert Israel, Apr 04 2024

Mathematica

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 *)

Prog

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

Crossrefs

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

Sequence in context: A121594 A163286 A022997 * A051121 A001356 A104811

Adjacent sequences: A256873 A256874 A256875 * A256877 A256878 A256879

Keyword

nonn,base

Author

M. F. Hasler, Apr 11 2015

Extensions

More terms from Robert Israel, Apr 04 2024

Status

approved