cp's OEIS Frontend

A360475 Smallest prime factor of (2^prime(n) + 1) / 3.

%I A360475 #24 Jan 27 2025 09:27:35
%S A360475 3,11,43,683,2731,43691,174763,2796203,59,715827883,1777,83,
%T A360475 2932031007403,283,107,2833,768614336404564651,7327657,56409643,1753,
%U A360475 201487636602438195784363,499,179,971,845100400152152934331135470251,415141630193,643,104124649,227
%N A360475 Smallest prime factor of (2^prime(n) + 1) / 3.
%C A360475 If (2^prime(n) + 1) / 3 is prime then a(n) is a Wagstaff prime (cf. A000979).
%C A360475 For n > 2, a(n) is congruent to 1 (mod 2*prime(n)).
%F A360475 a(n) = A020639(A126614(n)).
%e A360475 a(2)=3 since for prime(2)=3, (2^3+1)/3 = 3;
%e A360475 a(3)=11 since for prime(3)=5, (2^5+1)/3 = 11;
%e A360475 a(10)=59 since for prime(10)=29, (2^29+1)/3 = 59*3033169.
%p A360475 a:= n-> min(numtheory[factorset]((2^ithprime(n)+1)/3)):
%p A360475 seq(a(n), n=2..30);  # _Alois P. Heinz_, Feb 28 2023
%t A360475 a[n_] := FactorInteger[(2^Prime[n]+1)/3][[1, 1]];
%t A360475 Table[a[n], {n, 2, 30}] (* _Jean-François Alcover_, Jan 27 2025 *)
%o A360475 (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 A360475 Cf. A020639, A126614.
%K A360475 nonn
%O A360475 2,1
%A A360475 _Alain Rocchelli_, Feb 08 2023
%E A360475 a(26)-a(30) from _Amiram Eldar_, Feb 08 2023