

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.


2



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
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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..#s1]); 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



