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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.
2
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
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)
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Apr 11 2015
EXTENSIONS
More terms from Robert Israel, Apr 04 2024
STATUS
approved