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A000979 Wagstaff primes: primes of form (2^p + 1)/3.
(Formerly M2896 N1161)
29
3, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, 2932031007403, 768614336404564651, 201487636602438195784363, 845100400152152934331135470251, 56713727820156410577229101238628035243, 62357403192785191176690552862561408838653121833643 (list; graph; refs; listen; history; text; internal format)
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
P. Berrizbeitia, F. Luca, R. Melham, On a compositeness test for (2^p+1)/3, JIS 13 (2010) 10.1.7
C. Caldwell's The Top Twenty, Wagstaff.
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)
S. S. Wagstaff, Jr., The Cunningham Project.
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
Cf. A010051; subsequence of A007583.
Sequence in context: A135482 A360475 A126614 * A123628 A153476 A107290
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified June 14 19:19 EDT 2024. Contains 373401 sequences. (Running on oeis4.)