OFFSET
1,1
COMMENTS
Also, the primes with prime indices in the Jacobsthal sequence A001045.
Indices n such that (2^n + 1)/3 is prime are listed in A000978. - Alexander Adamchuk, Oct 03 2006
Primes in A126614. - Omar E. Pol, Nov 05 2013
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n=1..20
Herbert Batte, On Wagstaff primes in the k-Lucas number sequence, arXiv:2602.20387 [math.NT], 2026.
Pedro Berrizbeitia, Florian Luca, and Ray Melham, On a compositeness test for (2^p+1)/3, J. Int. Seq. 13 (2010), Art. 10.1.7.
Chris Caldwell's The Top Twenty, Wagstaff.
Alexey Dolotov, Three Brillhart-Lehmer-Selfridge primality proofs for Wagstaff numbers, arXiv:2605.18555 [math.NT], 2026.
Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
Editor's Note, Table of Wagstaff primes sent by D. H. Lehmer, Math. Mag., 27 (1954), 156-157.
Editor's Note, Table of Wagstaff primes sent by D. H. Lehmer (annotated and scanned copy)
Djurre G. Sikkema, Probable primality testing for Wagstaff prime, Bachelor's project mathematics, Univ. Groningen (Netherlands 2024). See p. 32.
Samuel S. Wagstaff, Jr., The Cunningham Project.
Samuel S. Wagstaff, Jr., Two Mersenne Prime Conjectures, J. Int. Seq. 28 (2025), Art. 25.7.2. See p. 2.
Wikipedia, Wagstaff prime
MATHEMATICA
Select[ Array[(2^# + 1)/3 &, 190], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Apr 03 2010 *)
PROG
(Haskell)
a000979 n = a000979_list !! (n-1)
a000979_list = filter ((== 1) . a010051) a007583_list
-- Reinhard Zumkeller, Mar 24 2013
(Python)
from gmpy2 import divexact
from sympy import prime, isprime
A000979 = [p for p in (divexact(2**prime(n)+1, 3) for n in range(2, 10**2)) if isprime(p)] # Chai Wah Wu, Sep 04 2014
(PARI) forprime(p=2, 10000, if(ispseudoprime(2^p\/3), print1(2^p\/3, ", "))) \\ Edward Jiang, Sep 05 2014
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
STATUS
approved