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A349667
Primes of the form 4*k+1 which are a prime after the Collatz step *3+1 and a maximal reduction by 2.
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
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
KEYWORD
nonn
AUTHOR
Karl-Heinz Hofmann, Dec 28 2021
STATUS
approved