A346136 a(n) is the number of iterations that n requires to reach 1 under the map n -> A346063(n).

0, 1, 2, 2, 3, 3, 1, 4, 1, 4, 3, 3, 4, 3, 2, 4, 4, 5, 2, 3, 9, 11, 8, 6, 10, 12, 6, 7, 2, 8, 4, 3, 6, 4, 10, 7, 2, 7, 4, 9, 4, 5, 4, 1, 8, 7, 6, 11, 2, 73, 5, 12, 5, 6, 1, 5, 2, 4, 34, 7, 5, 5, 2, 51, 7, 2, 5, 3, 5, 5, 3, 15, 6, 5, 2, 4, 10

Offset

1,3

Comments

Conjecture: the sequence is infinite.

Links

Table of n, a(n) for n=1..77.

Prog

(Python)
from sympy import prime, isprime
for n in range(1, 78):
    m = prime(n); ct = 0
    while m > 2:
        if isprime(m): m = m*m - 1; ct += 1
        else: m //= 2
    print(ct)
(PARI) f(x) = my(k=x^2-1); while(k>3 && !ispseudoprime(k), k\=2); k;
a(n) = my(c=0, x=prime(n)); while(x>2, c++; x=f(x)); c; \\ Jinyuan Wang, Jul 15 2022

Crossrefs

Cf. A339991, A340008, A340418, A340419, A346063.

Sequence in context: A230040 A242361 A116464 * A284532 A125585 A327236

Adjacent sequences: A346133 A346134 A346135 * A346137 A346138 A346139

Keyword

nonn,more

Author

Ya-Ping Lu, Jul 05 2021

Extensions

a(1) corrected by Jinyuan Wang, Jul 15 2022

Status

approved