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A334676 a(n) is the least number that can be reached starting from n and iterating the nondeterministic map x -> x/d where d is a nonzero digit of x dividing x.

%I A334676 #39 Aug 23 2025 12:36:06
%S A334676 1,1,1,1,1,1,1,1,1,10,11,1,13,14,1,16,17,18,19,10,21,11,23,1,1,13,27,
%T A334676 14,29,10,31,16,11,34,1,1,37,38,13,10,41,21,43,11,1,46,47,1,49,10,51,
%U A334676 13,53,54,11,56,57,58,59,10,61,31,21,16,13,11,67,68,69
%N A334676 a(n) is the least number that can be reached starting from n and iterating the nondeterministic map x -> x/d where d is a nonzero digit of x dividing x.
%C A334676 See A336580 for the positions of 1's.
%H A334676 Rémy Sigrist, <a href="/A334676/b334676.txt">Table of n, a(n) for n = 1..10000</a>
%F A334676 a(a(n)) = a(n).
%e A334676 For n = 168:
%e A334676 - 168 / 6 = 28, 28 / 2 = 14,
%e A334676 - 168 / 8 = 21,
%e A334676 - so a(168) = 14.
%o A334676 (PARI) for (n=1, #a=vector(69, k, k), apply (d -> a[n]=min(a[n], a[n/d]), setintersect(Set(digits(n)), divisors(n))); print1 (a[n]", "))
%o A334676 (Python)
%o A334676 def neighs(x):
%o A334676     yield from (x//d for d in list(map(int, str(x))) if d > 0 and x%d == 0)
%o A334676 def A334676(n):
%o A334676     reach, expand = {n}, [n]
%o A334676     while expand:
%o A334676         q = expand.pop()
%o A334676         for r in neighs(q):
%o A334676             if r not in reach:
%o A334676                 reach.add(r)
%o A334676                 expand.append(r)
%o A334676     return min(reach)
%o A334676 print([A334676(n) for n in range(1, 70)]) # _Michael S. Branicky_, Aug 23 2025
%Y A334676 See A334684 for a similar sequence.
%Y A334676 Cf. A336580.
%K A334676 nonn,base,changed
%O A334676 1,10
%A A334676 _Rémy Sigrist_, Jul 25 2020