A363673 - OEIS

%I #12 Jun 26 2023 14:48:00

%S 5,7,11,43,23,2731,43691,174763,47,59,715827883,223,83,431,283,107,

%T 2833,768614336404564651,7327657,228479,439,2687,167,179,971,

%U 7432339208719,2550183799,643,104124649,227,56713727820156410577229101238628035243,263,1097,4506937,1193,18121,15073,150287

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

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

%e For n=2, prime(2)=3 and a(2)=7 since 2^(2*3)-1 = 63 = 3^2*7.

%e For n=4, prime(4)=7 and a(4)=43 since 2^(2*7)-1 = 16383 = 3*43*127.

%e For n=5, prime(5)=11 and a(5)=23 since 2^(2*11)-1 = 4194303 = 3*23*89*683.

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

%o (Python)

%o from sympy import prime, primefactors

%o def A363673(n):

%o     m = (1<<(prime(n)<<1))-1

%o     a, b = divmod(m,3)

%o     while not b:

%o         m = a

%o         a, b = divmod(m,3)

%o     return min(primefactors(m)) # _Chai Wah Wu_, Jun 26 2023

%Y Cf. A152099.

%K nonn

%O 1,1

%A _Alain Rocchelli_, Jun 14 2023