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

1,1

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).

Links

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

Example

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

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 *)

Prog

(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=", ")

Crossrefs

Cf. A002144, A002145, A349666.

Sequence in context: A156343 A154762 A079348 * A174024 A061381 A048520

Adjacent sequences: A349664 A349665 A349666 * A349668 A349669 A349670

Keyword

nonn

Author

Karl-Heinz Hofmann, Dec 28 2021

Status

approved