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

%I A363673 #12 Jun 26 2023 14:48:00
%S A363673 5,7,11,43,23,2731,43691,174763,47,59,715827883,223,83,431,283,107,
%T A363673 2833,768614336404564651,7327657,228479,439,2687,167,179,971,
%U A363673 7432339208719,2550183799,643,104124649,227,56713727820156410577229101238628035243,263,1097,4506937,1193,18121,15073,150287
%N A363673 a(n) is the least prime factor (> 3) in the factorization of 2^(2*prime(n))-1.
%C A363673 2*prime(n)+1 is prime iff a(n) = 2*prime(n)+1.
%e A363673 For n=2, prime(2)=3 and a(2)=7 since 2^(2*3)-1 = 63 = 3^2*7.
%e A363673 For n=4, prime(4)=7 and a(4)=43 since 2^(2*7)-1 = 16383 = 3*43*127.
%e A363673 For n=5, prime(5)=11 and a(5)=23 since 2^(2*11)-1 = 4194303 = 3*23*89*683.
%o A363673 (PARI) forprime(p=2, 163, Ap=factor(2^(2*p)-1)[2,1]; print1(Ap,", "))
%o A363673 (Python)
%o A363673 from sympy import prime, primefactors
%o A363673 def A363673(n):
%o A363673     m = (1<<(prime(n)<<1))-1
%o A363673     a, b = divmod(m,3)
%o A363673     while not b:
%o A363673         m = a
%o A363673         a, b = divmod(m,3)
%o A363673     return min(primefactors(m)) # _Chai Wah Wu_, Jun 26 2023
%Y A363673 Cf. A152099.
%K A363673 nonn
%O A363673 1,1
%A A363673 _Alain Rocchelli_, Jun 14 2023