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%I #30 Jan 03 2022 17:14:27
%S 13,17,29,37,41,53,61,89,97,101,109,137,149,157,181,197,229,241,257,
%T 269,277,281,349,389,397,409,421,449,461,509,577,617,661,677,701,757,
%U 761,769,809,829,853,857,881,941,977,1009,1021,1049,1061,1069,1097,1109,1117,1181
%N Primes of the form 4*k+1 which are a prime after the Collatz step *3+1 and a maximal reduction by 2.
%C Pythagorean primes (A002144) of the form 4*k+1 have, after the Collatz step *3+1, at least 2 or more factors 2. (See also A349666).
%H Karl-Heinz Hofmann, <a href="/A349667/b349667.txt">Table of n, a(n) for n = 1..10000</a>
%e a(41) = 853; 853*3+1 = 2560; then dividing 9 times by 2 = 5, a prime.
%t f[n_] := n/2^IntegerExponent[n, 2]; q[n_] := PrimeQ[n] && PrimeQ[f[3*n + 1]]; Select[4 * Range[300] + 1, q] (* _Amiram Eldar_, Jan 03 2022 *)
%o (Python)
%o from sympy import isprime
%o for p in range(1,10000,4):
%o if isprime(p):
%o p2 = (3 * p + 1)
%o while p2 % 2 == 0: p2 //= 2
%o if isprime(p2): print(p, end=", ")
%Y Cf. A002144, A002145, A349666.
%K nonn
%O 1,1
%A _Karl-Heinz Hofmann_, Dec 28 2021
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