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a(n) is the prime reached after A354747(n) steps when repeatedly applying the map x -> 3*x+2 to 2*n-1, or 0 if no prime is ever reached.
2

%I #8 Jul 01 2022 22:16:23

%S 5,11,17,23,29,107,41,47,53,59,197,71,233,83,89,863,101,107,113,359,

%T 2480057,131,137,431,149,467,4373,167,173,179,557,191,197,5507,1889,

%U 647,1997,227,233,239,2213,251,257,263,269,827,281,863,293,2699,2753,311,317

%N a(n) is the prime reached after A354747(n) steps when repeatedly applying the map x -> 3*x+2 to 2*n-1, or 0 if no prime is ever reached.

%C Is a(100943) = 0?

%C If not 0, a(100943) >= 10^10000. - _Michael S. Branicky_, Jun 07 2022

%o (PARI) a(n) = my(x=2*n-1); while(1, x=3*x+2; if(ispseudoprime(x), return(x)))

%o (Python)

%o from sympy import isprime

%o def f(x): return 3*x + 2

%o def a(n):

%o fn, c = f(2*n-1), 1

%o while not isprime(fn): fn, c = f(fn), c+1

%o return fn

%o print([a(n) for n in range(1, 54)]) # _Michael S. Branicky_, Jun 07 2022

%Y Cf. A052333, A354747.

%K nonn

%O 1,1

%A _Felix Fröhlich_, Jun 06 2022