A343156 - OEIS

%I #32 Dec 31 2023 12:35:25

%S 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,

%T 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,

%U 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

%N 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.

%C 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.

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

%H Hans Havermann, <a href="/A343156/b343156.txt">Table of n, a(n) for n = 2..406</a>

%e 10 = 2*5 -> 25 = 5^2 -> 5, prime, taking two steps, so a(10)=2.

%e a(91) = 64: see A084319.

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

%Y See A343158 for when k first appears.

%K nonn,base

%O 2,9

%A _N. J. A. Sloane_, Apr 07 2021