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

Author

N. J. A. Sloane, Apr 07 2021

Keywords

• nonn
• base

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.

Examples

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

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

Crossrefs

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

See A343158 for when k first appears.