A349667 Primes of the form 4*k+1 which are a prime after the Collatz step *3+1 and a maximal reduction by 2.

13, 17, 29, 37, 41, 53, 61, 89, 97, 101, 109, 137, 149, 157, 181, 197, 229, 241, 257, 269, 277, 281, 349, 389, 397, 409, 421, 449, 461, 509, 577, 617, 661, 677, 701, 757, 761, 769, 809, 829, 853, 857, 881, 941, 977, 1009, 1021, 1049, 1061, 1069, 1097, 1109, 1117, 1181

Offset: 1

Author

Karl-Heinz Hofmann, Dec 28 2021

Keywords

• nonn

Comments

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).

Examples

			a(41) = 853; 853*3+1 = 2560; then dividing 9 times by 2 = 5, a prime.
		

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002144, A002145, A349666.

Programs

Mathematica

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 *)

Python

from sympy import isprime
for p in range(1,10000,4):
    if isprime(p):
        p2 = (3 * p + 1)
        while p2 % 2 == 0: p2 //= 2
        if isprime(p2): print(p, end=", ")