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

1,2

Links

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

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.

Example

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

Prog

(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]", ")) }

Crossrefs

See A334676 for a similar sequence.

Sequence in context: A043271 A333921 A278063 * A062759 A327526 A121758

Adjacent sequences: A334681 A334682 A334683 * A334685 A334686 A334687

Keyword

nonn,base

Author

Rémy Sigrist, Jul 25 2020

Status

approved