A334684 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 proper divisor of x whose decimal representation appears in that of x.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 6, 13, 14, 3, 16, 17, 18, 19, 10, 21, 11, 23, 6, 5, 13, 27, 14, 29, 10, 31, 16, 11, 34, 7, 6, 37, 38, 13, 10, 41, 21, 43, 11, 9, 46, 47, 6, 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

Examples

			For n = 140:
- 140 / 4 = 35, 35 / 5 = 7,
- 140 / 14 = 10,
- so a(140) = 7.
		

Links

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

Crossrefs

See A334676 for a similar sequence.

Programs

PARI

{ for (n=1, #a=vector(69, k, k), d=digits(n); s=setintersect(divisors(n), setbinop((u,v)->fromdigits(d[u..v]), [1..#d])); apply (t -> a[n]=min(a[n], a[n/t]), s[1..#s-1]); print1 (a[n]", ")) }

Formula

a(a(n)) = n.

a(10*k) <= 10 for any k > 0.

a(5^k) = 5 for any k > 0.

a(p) = p for any prime number p.