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%I #21 Mar 05 2023 12:05:56
%S 3,11,43,683,2731,43691,174763,2796203,59,715827883,1777,83,
%T 2932031007403,283,107,2833,768614336404564651,7327657,56409643,1753,
%U 201487636602438195784363,499,179,971,845100400152152934331135470251,415141630193,643,104124649,227
%N Smallest prime factor of (2^prime(n) + 1) / 3.
%C If (2^prime(n) + 1) / 3 is prime then a(n) is a Wagstaff prime (cf. A000979).
%C For n > 2, a(n) is congruent to 1 (mod 2*prime(n)).
%F a(n) = A020639(A126614(n)).
%e a(2)=3 since for prime(2)=3, (2^3+1)/3 = 3;
%e a(3)=11 since for prime(3)=5, (2^5+1)/3 = 11;
%e a(10)=59 since for prime(10)=29, (2^29+1)/3 = 59*3033169.
%p a:= n-> min(numtheory[factorset]((2^ithprime(n)+1)/3)):
%p seq(a(n), n=2..30); # _Alois P. Heinz_, Feb 28 2023
%o (PARI) forprime(p=3, 100, An=(2^p+1)/3; if(isprime(An), print1(An,", "), forprime(div=3, 2^((p-1)/2), if(An%div==0, print1(div,", "); next(2)))))
%Y Cf. A020639, A126614.
%K nonn
%O 2,1
%A _Alain Rocchelli_, Feb 08 2023
%E a(26)-a(30) from _Amiram Eldar_, Feb 08 2023
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