A256875 Numbers divisible by prime(d) for each digit d in their base-5 representation, none of which may be zero.

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

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

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

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

Sequence in context: A264955 A038266 A298881 * A117596 A276601 A096377

Adjacent sequences: A256872 A256873 A256874 * A256876 A256877 A256878

Keyword

nonn,base

Author

M. F. Hasler, Apr 11 2015

Status

approved