A256869 Numbers divisible by prime(d+1) for each digit d of their base-9 representation.

0, 20, 84, 90, 180, 252, 273, 455, 510, 738, 756, 810, 816, 840, 900, 1224, 1275, 1460, 1470, 1620, 1640, 2090, 2185, 2268, 2450, 2541, 3080, 3289, 3553, 4199, 4590, 5434, 6570, 6642, 6660, 6804, 7290, 7326, 7344, 7380, 7395, 7470, 7560, 7866, 8100, 8160, 8190, 8778, 8841, 8925, 9282

Offset: 1

Author

M. F. Hasler, Apr 11 2015

Keywords

• nonn
• base

Comments

The base-9 variant of A256882 - A256884, A256866 - A256870 in bases 2, ..., 10.

A variant of A256879 where digits 0 are forbidden and divisibility by prime(d) is required.

From Robert Israel, Aug 01 2019: (Start)

If n is in the sequence and is even, then 9*n is in the sequence.

If n is in the sequence and 9^k > n, then (9^k+1)*n is in the sequence.

All multiples of 223092870 are in the sequence.

(End)

Links

• Robert Israel, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A256882, A256883, A256884, A256865-A256870, A256874-A256879, A256786.

Programs

Maple

P:= [seq(ithprime(i),i=1..9)]:
filter:= proc(n) local L;
  L:= convert(convert(n,base,9),set);
  L:= map(t -> P[t+1],L);
  n mod convert(L,`*`) = 0
end proc:
select(filter, [$0..10000]); # Robert Israel, Aug 01 2019

PARI

is(n,b=9)=!for(i=1,#d=Set(digits(n,b)),n%prime(d[i]+1)&&return)

Formula

a(n) ~ 223092870*n. - Robert Israel, Aug 01 2019