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

%I A346136 #9 Jul 15 2022 04:07:23
%S A346136 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,
%T A346136 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,
%U A346136 7,2,5,3,5,5,3,15,6,5,2,4,10
%N A346136 a(n) is the number of iterations that n requires to reach 1 under the map n -> A346063(n).
%C A346136 Conjecture: the sequence is infinite.
%o A346136 (Python)
%o A346136 from sympy import prime, isprime
%o A346136 for n in range(1, 78):
%o A346136     m = prime(n); ct = 0
%o A346136     while m > 2:
%o A346136         if isprime(m): m = m*m - 1; ct += 1
%o A346136         else: m //= 2
%o A346136     print(ct)
%o A346136 (PARI) f(x) = my(k=x^2-1); while(k>3 && !ispseudoprime(k), k\=2); k;
%o A346136 a(n) = my(c=0, x=prime(n)); while(x>2, c++; x=f(x)); c; \\ _Jinyuan Wang_, Jul 15 2022
%Y A346136 Cf. A339991, A340008, A340418, A340419, A346063.
%K A346136 nonn,more
%O A346136 1,3
%A A346136 _Ya-Ping Lu_, Jul 05 2021
%E A346136 a(1) corrected by _Jinyuan Wang_, Jul 15 2022