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

%I A256869 #20 Dec 13 2024 13:22:24
%S A256869 0,20,84,90,180,252,273,455,510,738,756,810,816,840,900,1224,1275,
%T A256869 1460,1470,1620,1640,2090,2185,2268,2450,2541,3080,3289,3553,4199,
%U A256869 4590,5434,6570,6642,6660,6804,7290,7326,7344,7380,7395,7470,7560,7866,8100,8160,8190,8778,8841,8925,9282
%N A256869 Numbers divisible by prime(d+1) for each digit d of their base-9 representation.
%C A256869 The base-9 variant of A256882 - A256884, A256866 - A256870 in bases 2, ..., 10.
%C A256869 A variant of A256879 where digits 0 are forbidden and divisibility by prime(d) is required.
%C A256869 From _Robert Israel_, Aug 01 2019: (Start)
%C A256869 If n is in the sequence and is even, then 9*n is in the sequence.
%C A256869 If n is in the sequence and 9^k > n, then (9^k+1)*n is in the sequence.
%C A256869 All multiples of 223092870 are in the sequence.
%C A256869 (End)
%H A256869 Robert Israel, <a href="/A256869/b256869.txt">Table of n, a(n) for n = 1..3000</a>
%F A256869 a(n) ~ 223092870*n. - _Robert Israel_, Aug 01 2019
%p A256869 P:= [seq(ithprime(i),i=1..9)]:
%p A256869 filter:= proc(n) local L;
%p A256869   L:= convert(convert(n,base,9),set);
%p A256869   L:= map(t -> P[t+1],L);
%p A256869   n mod convert(L,`*`) = 0
%p A256869 end proc:
%p A256869 select(filter, [$0..10000]); # _Robert Israel_, Aug 01 2019
%o A256869 (PARI) is(n,b=9)=!for(i=1,#d=Set(digits(n,b)),n%prime(d[i]+1)&&return)
%Y A256869 Cf. A256882, A256883, A256884, A256865-A256870, A256874-A256879, A256786.
%K A256869 nonn,base
%O A256869 1,2
%A A256869 _M. F. Hasler_, Apr 11 2015