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.

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, 14, 29, 10, 31, 16, 11, 34, 1, 1, 37, 38, 13, 10, 41, 21, 43, 11, 1, 46, 47, 1, 49, 10, 51, 13, 53, 54, 11, 56, 57, 58, 59, 10, 61, 31, 21, 16, 13, 11, 67, 68, 69

Offset

1,10

Comments

See A336580 for the positions of 1's.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Formula

a(a(n)) = a(n).

Example

For n = 168:
- 168 / 6 = 28, 28 / 2 = 14,
- 168 / 8 = 21,
- so a(168) = 14.

Prog

(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]", "))
(Python)
def neighs(x):
    yield from (x//d for d in list(map(int, str(x))) if d > 0 and x%d == 0)
def A334676(n):
    reach, expand = {n}, [n]
    while expand:
        q = expand.pop()
        for r in neighs(q):
            if r not in reach:
                reach.add(r)
                expand.append(r)
    return min(reach)
print([A334676(n) for n in range(1, 70)]) # Michael S. Branicky, Aug 23 2025

Crossrefs

See A334684 for a similar sequence.

Cf. A336580.

Sequence in context: A284201 A324660 A336035 * A385105 A176998 A328752

Adjacent sequences: A334673 A334674 A334675 * A334677 A334678 A334679

Keyword

nonn,base

Author

Rémy Sigrist, Jul 25 2020

Status

approved