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

Author

Rémy Sigrist, Jul 25 2020

Keywords

• nonn
• base
• changed

Comments

See A336580 for the positions of 1's.

Examples

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

Links

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

Crossrefs

See A334684 for a similar sequence.

Cf. A336580.

Programs

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

Formula

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