A349667 - OEIS

%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