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
Keywords
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
Programs
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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 *)
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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=", ")
Comments