A256868 -id:A256868 - cp's OEIS frontend

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

M. F. Hasler, Apr 11 2015

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

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

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

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

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 *)

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

More terms from Robert Israel, Apr 04 2024

A256878 Numbers divisible by prime(d) for each digit d in their base-8 representation, none of which may be zero.

Original entry on oeis.org

18, 35, 78, 84, 90, 138, 210, 255, 330, 429, 588, 594, 910, 1098, 1170, 1275, 1386, 1530, 1755, 1820, 1950, 2156, 2275, 2706, 3315, 3510, 3927, 3978, 4746, 4758, 4794, 4900, 4914, 5202, 5610, 5850, 6244, 6300, 6412, 6930, 7254, 7410, 7462, 7566, 8778, 8850, 9042, 9354, 9435, 9492

Offset: 1

M. F. Hasler, Apr 11 2015

Base-8 analog of A256786. See A256874 - A256879 for the base-4, ..., base-9 analogs.

See A256868 for a variant where divisibility by prime(d+1) is required instead.

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

is(n,b=8)=!for(i=1,#d=Set(digits(n,b)),(!d[i]||n%prime(d[i]))&&return)

cp's OEIS Frontend

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

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