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

Author

M. F. Hasler, Apr 11 2015

Keywords

• nonn
• base

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

Crossrefs

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

Programs

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

PARI

is(n,b=5)=!for(i=1,#d=Set(digits(n,b)),(!d[i]||n%prime(d[i]))&&return)