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

3, 11, 43, 683, 2731, 43691, 174763, 2796203, 59, 715827883, 1777, 83, 2932031007403, 283, 107, 2833, 768614336404564651, 7327657, 56409643, 1753, 201487636602438195784363, 499, 179, 971, 845100400152152934331135470251, 415141630193, 643, 104124649, 227

Offset

2,1

Comments

If (2^prime(n) + 1) / 3 is prime then a(n) is a Wagstaff prime (cf. A000979).

For n > 2, a(n) is congruent to 1 (mod 2*prime(n)).

Links

Table of n, a(n) for n=2..30.

Formula

a(n) = A020639(A126614(n)).

Example

a(2)=3 since for prime(2)=3, (2^3+1)/3 = 3;
a(3)=11 since for prime(3)=5, (2^5+1)/3 = 11;
a(10)=59 since for prime(10)=29, (2^29+1)/3 = 59*3033169.

Maple

a:= n-> min(numtheory[factorset]((2^ithprime(n)+1)/3)):
seq(a(n), n=2..30);  # Alois P. Heinz, Feb 28 2023

Prog

(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)))))

Crossrefs

Cf. A020639, A126614.

Sequence in context: A349058 A051257 A135482 * A126614 A000979 A123628

Adjacent sequences: A360472 A360473 A360474 * A360476 A360477 A360478

Keyword

nonn

Author

Alain Rocchelli, Feb 08 2023

Extensions

a(26)-a(30) from Amiram Eldar, Feb 08 2023

Status

approved