A343156 Starting at n, a(n) = number of iterations of the map x -> A084317(x) (concatenate distinct prime factors of x) required to reach a prime, or -1 if no prime is ever reached.

0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 1, 0, 2, 4, 1, 0, 1, 0, 2, 1, 1, 0, 1, 1, 4, 1, 2, 0, 2, 0, 1, 1, 5, 3, 1, 0, 2, 1, 2, 0, 2, 0, 1, 4, 1, 0, 1, 1, 2, 1, 4, 0, 1, 2, 2, 2, 1, 0, 2, 0, 3, 1, 1, 3, 1, 0, 5, 3, 1, 0, 1, 0, 2, 4, 2, 2, 2, 0, 2, 1, 1, 0, 2, 3, 2, 3, 1, 0, 2, 64, 1, 1, 2, 4, 1, 0, 2, 1, 2

Offset

2,9

Comments

Judging by the behavior of similar sequences, it is likely that almost all values of a(n) are -1. n = 407 (see A343157) seems to be the first open case.

References

Eric Angelini, W. Edwin Clark, Hans Havermann, Frank Stevenson, Allan C. Wechsler, and others, Postings to Math Fun mailing list, April 2021.

Links

Hans Havermann, Table of n, a(n) for n = 2..406

Example

10 = 2*5 -> 25 = 5^2 -> 5, prime, taking two steps, so a(10)=2.
a(91) = 64: see A084319.

Crossrefs

Cf. A084317, A037274, A037276, A084319, A195264, A343157.

See A343158 for when k first appears.

Sequence in context: A072662 A030010 A321297 * A163577 A132178 A357869

Adjacent sequences: A343153 A343154 A343155 * A343157 A343158 A343159

Keyword

nonn,base

Author

N. J. A. Sloane, Apr 07 2021

Status

approved