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A000979 Wagstaff primes: primes of form (2^p + 1)/3.

%I A000979 M2896 N1161 #73 Aug 23 2024 12:17:06
%S A000979 3,11,43,683,2731,43691,174763,2796203,715827883,2932031007403,
%T A000979 768614336404564651,201487636602438195784363,
%U A000979 845100400152152934331135470251,56713727820156410577229101238628035243,62357403192785191176690552862561408838653121833643
%N A000979 Wagstaff primes: primes of form (2^p + 1)/3.
%C A000979 Also, the primes with prime indices in the Jacobsthal sequence A001045.
%C A000979 Indices n such that (2^n + 1)/3 is prime are listed in A000978. - _Alexander Adamchuk_, Oct 03 2006
%C A000979 Primes in A126614. - _Omar E. Pol_, Nov 05 2013
%D A000979 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000979 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000979 T. D. Noe, <a href="/A000979/b000979.txt">Table of n, a(n) for n=1..20</a>
%H A000979 P. Berrizbeitia, F. Luca, and R. Melham, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Luca/luca33.html">On a compositeness test for (2^p+1)/3</a>, JIS 13 (2010) 10.1.7
%H A000979 C. Caldwell's The Top Twenty, <a href="https://t5k.org/top20/page.php?id=67">Wagstaff</a>.
%H A000979 Ernest G. Hibbs, <a href="https://www.proquest.com/openview/4012f0286b785cd732c78eb0fc6fce80">Component Interactions of the Prime Numbers</a>, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
%H A000979 Editor's Note, <a href="http://www.jstor.org/stable/3029104">Table of Wagstaff primes sent by D. H. Lehmer</a>, Math. Mag., 27 (1954), 156-157.
%H A000979 Editor's Note, <a href="/A000979/a000979.pdf">Table of Wagstaff primes sent by D. H. Lehmer</a> (annotated and scanned copy)
%H A000979 Djurre G. Sikkema, <a href="https://fse.studenttheses.ub.rug.nl/33908">Probable primality testing for Wagstaff prime</a>, Bachelor's project mathematics, Univ. Groningen (Netherlands 2024). See p. 32.
%H A000979 S. S. Wagstaff, Jr., <a href="http://homes.cerias.purdue.edu/~ssw/cun/index.html">The Cunningham Project</a>.
%H A000979 Wikipedia, <a href="http://en.wikipedia.org/wiki/Wagstaff_prime">Wagstaff prime</a>
%t A000979 Select[ Array[(2^# + 1)/3 &, 190], PrimeQ] (* _Vladimir Joseph Stephan Orlovsky_, Apr 03 2010 *)
%o A000979 (Haskell)
%o A000979 a000979 n = a000979_list !! (n-1)
%o A000979 a000979_list = filter ((== 1) . a010051) a007583_list
%o A000979 -- _Reinhard Zumkeller_, Mar 24 2013
%o A000979 (Python)
%o A000979 from gmpy2 import divexact
%o A000979 from sympy import prime, isprime
%o A000979 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
%o A000979 (PARI) forprime(p=2,10000,if(ispseudoprime(2^p\/3),print1(2^p\/3,","))) \\ _Edward Jiang_, Sep 05 2014
%Y A000979 Cf. A000978, A049883, A001045, A127962.
%Y A000979 Cf. A010051; subsequence of A007583.
%K A000979 nonn
%O A000979 1,1
%A A000979 _N. J. A. Sloane_