A039687 Primes of the form 3*2^k + 1.

7, 13, 97, 193, 769, 12289, 786433, 3221225473, 206158430209, 6597069766657, 221360928884514619393, 2353913150770005286438421033702874906038383291674012942337

Offset: 1

Author

Felice Russo

Keywords

• nonn

Comments

Primes of the form 6m+1 (A002476) of A074781. - Bernard Schott, Dec 14 2020

Links

• S. W. Golomb, Properties of the sequence 3*2^n+1, Math. Comp., 30 (1976), 657-663.
• S. W. Golomb, Properties of the sequence 3*2^n+1, Math. Comp., 30 (1976), 657-663. [Annotated scanned copy]
• Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.

Crossrefs

For more terms see A002253. These are the primes in A004119 (or A181565).

Cf. A002476, A074781.

Subsequence of A081091.

Programs

Mathematica

Select[Table[6 2^n+1,{n,0,250}],PrimeQ] (* Harvey P. Dale, Dec 17 2010 *)

PARI

A039687(n)=3<<A002253(n)+1 \\ M. F. Hasler, Mar 03 2023

Formula

a(n) = 3*2^A002253(n) + 1. - M. F. Hasler, Mar 03 2023