A363673 a(n) is the least prime factor (> 3) in the factorization of 2^(2*prime(n))-1.

5, 7, 11, 43, 23, 2731, 43691, 174763, 47, 59, 715827883, 223, 83, 431, 283, 107, 2833, 768614336404564651, 7327657, 228479, 439, 2687, 167, 179, 971, 7432339208719, 2550183799, 643, 104124649, 227, 56713727820156410577229101238628035243, 263, 1097, 4506937, 1193, 18121, 15073, 150287

Offset: 1

Author

Alain Rocchelli, Jun 14 2023

Keywords

• nonn

Comments

2*prime(n)+1 is prime iff a(n) = 2*prime(n)+1.

Examples

			For n=2, prime(2)=3 and a(2)=7 since 2^(2*3)-1 = 63 = 3^2*7.
For n=4, prime(4)=7 and a(4)=43 since 2^(2*7)-1 = 16383 = 3*43*127.
For n=5, prime(5)=11 and a(5)=23 since 2^(2*11)-1 = 4194303 = 3*23*89*683.
		

Crossrefs

Cf. A152099.

Programs

PARI

forprime(p=2, 163, Ap=factor(2^(2*p)-1)[2,1]; print1(Ap,", "))

Python

from sympy import prime, primefactors
def A363673(n):
    m = (1<<(prime(n)<<1))-1
    a, b = divmod(m,3)
    while not b:
        m = a
        a, b = divmod(m,3)
    return min(primefactors(m)) # Chai Wah Wu, Jun 26 2023