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A256875
Numbers divisible by prime(d) for each digit d in their base-5 representation, none of which may be zero.
3
6, 12, 36, 156, 162, 186, 282, 306, 312, 546, 784, 786, 906, 912, 924, 936, 1246, 1536, 1806, 2674, 2814, 2856, 3906, 3912, 3936, 4032, 4056, 4062, 4074, 4284, 4536, 4656, 4662, 4686, 4746, 4914, 5796, 5922, 6174, 7032, 7056, 7062, 7182, 7434, 7656, 7662, 7686, 7782, 7806, 7812, 8064, 8106, 8946, 9072, 9114, 9282, 9324
OFFSET
1,1
COMMENTS
Base-5 analog of A256786. See A256874 - A256879 for the base-3, ..., base-9 analogs.
See A256865 for a variant where divisibility by prime(d+1) is required instead.
From Robert Israel, Apr 04 2024: (Start)
Since digit 0 is not allowed, terms can't be divisible by 5, so digit 3 is also not allowed.
All terms are even. (End)
LINKS
MAPLE
P:= [seq(ithprime(i), i=1..4)]:
filter:= proc(n) local S, s;
S:= convert(convert(n, base, 5), set);
if member(0, S) then return false fi;
n mod mul(P[s], s=S) = 0
end proc:
select(filter, [$1..10^4]); # Robert Israel, Apr 04 2024
PROG
(PARI) is(n, b=5)=!for(i=1, #d=Set(digits(n, b)), (!d[i]||n%prime(d[i]))&&return)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Apr 11 2015
STATUS
approved