

A000979


Wagstaff primes: primes of form (2^p + 1)/3.
(Formerly M2896 N1161)


27



3, 11, 43, 683, 2731, 43691, 174763, 2796203, 715827883, 2932031007403, 768614336404564651, 201487636602438195784363, 845100400152152934331135470251, 56713727820156410577229101238628035243, 62357403192785191176690552862561408838653121833643
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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
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.
Editor's Note, Table of Wagstaff primes sent by D. H. Lehmer, Math. Mag., 27 (1954), 156157.
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 !! (n1)
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. A000978, A049883, A001045, A127962.
Cf. A010051; subsequence of A007583.
Sequence in context: A051257 A135482 A126614 * A123628 A153476 A107290
Adjacent sequences: A000976 A000977 A000978 * A000980 A000981 A000982


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


STATUS

approved



