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A244356 Numbers n such that n and n+1 are not divisible by any of their nonzero digits.

%I A244356 #17 May 22 2025 10:21:39
%S A244356 37,46,53,56,57,58,67,68,73,78,86,97,307,337,346,358,373,376,379,388,
%T A244356 397,406,429,433,446,457,466,469,473,477,478,489,493,498,506,507,508,
%U A244356 538,553,556,557,558,577,578,586,587,588,596,597,598,646,656,657,658,667,668,669
%N A244356 Numbers n such that n and n+1 are not divisible by any of their nonzero digits.
%C A244356 This is a subsequence of A038772.
%C A244356 All numbers end in a 3, 6, 7, 8, or 9.
%H A244356 Robert Israel, <a href="/A244356/b244356.txt">Table of n, a(n) for n = 1..10000</a>
%e A244356 37 is not divisible by 3 or 7 and 38 is not divisible by 3 or 8. Thus 37 is a member of this sequence.
%p A244356 filter:= proc(n) local L;
%p A244356   L:= convert(convert(n,base,10), set) minus {0};
%p A244356   not ormap(t -> n mod t = 0, L)
%p A244356 end proc:
%p A244356 B:= select(filter, {$1..1000}):
%p A244356 sort(convert(B intersect map(`-`,B,1), list)); # _Robert Israel_, Dec 08 2019
%o A244356 (Python)
%o A244356 def a(n):
%o A244356   for i in range(10**3):
%o A244356     tot = 0
%o A244356     for k in range(i,i+n):
%o A244356       c = 0
%o A244356       for b in str(k):
%o A244356         if b != '0':
%o A244356           if k%int(b)!=0:
%o A244356             c += 1
%o A244356       if c == len(str(k))-str(k).count('0'):
%o A244356         tot += 1
%o A244356     if tot == n:
%o A244356       print(i,end=', ')
%o A244356 a(2)
%Y A244356 Cf. A038772, A237766.
%K A244356 nonn,base,look
%O A244356 1,1
%A A244356 _Derek Orr_, Jun 26 2014