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

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..12.

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.

Formula

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

Mathematica

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

Prog

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

Crossrefs

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

Cf. A002476, A074781.

Subsequence of A081091.

Sequence in context: A132373 A110293 A253333 * A001544 A202152 A136720

Adjacent sequences: A039684 A039685 A039686 * A039688 A039689 A039690

Keyword

nonn

Author

Felice Russo

Status

approved