1,1

Jun 18 2008: Vincent Diepeveen (diep(AT)xs4all.nl) writes that he has found that (2^986191+1)/3 is a strong PRP, although it may not correspond to the next term. All exponents n=2 up to n=829k have been searched with a single check.

It is easy to see that the definition implies that n must be an odd prime. - N. J. A. Sloane (njas(AT)research.att.com), Oct 06 2006

The terms from a(30)=42737 on only give probable primes. Caldwell lists the largest certified primes. - Jens Kruse Andersen (jens.k.a(AT)get2net.dk), Jan 11 2006

Prime numbers of the form 1+Sum_{i=1..m} [2^(2i-1)]. - Artur Jasinski (grafix(AT)csl.pl), Feb 09 2007

There is a new conjecture stating that a Wagstaff number is prime under the following condition (based on DiGraph cycles under the LLT): Let p be a prime integer > 3, Np = 2^p+1 and Wp = N/3, S(0) = 3/2 (or 1/4) and S(i+1) = S(i)^2 - 2 (mod Np). Then Wp is prime iff S(p-1) == S(0) (mod Wp) . - Tony Reix (tony.reix(AT)laposte.net), Sep 03 2007

a(40) was found by Vincent Diepeveen (see PRP Top Records link). - a(40) from Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 19 2008

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 2nd edition, 1985; and later supplements.

Problem 174, "A solution in primes", Math. Mag., 27 (1954), 156-157.

S. S. Wagstaff, Jr., personal communication.

J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

C. Caldwell's The Top Twenty, Wagstaff.

C. Caldwell, New Mersenne Conjecture

H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.

H. Lifchitz, Mersenne and Fermat primes field

Henri & Renaud Lifchitz, PRP Records.

S. S. Wagstaff, Jr., The Cunningham Project

Eric Weisstein's World of Mathematics, Repunit

Eric Weisstein's World of Mathematics, Wagstaff Prime

Eric Weisstein's World of Mathematics, Integer Sequence Primes

Wikipedia, Wagstaff prime

H. & R. Lifchitz PRP Top Records.

a(n) = A107036(n) for n>1. - Alexander Adamchuk (alex(AT)kolmogorov.com), Feb 10 2007

a = {}; Do[c = 1 + Sum[2^(2n - 1), {n, 1, x}]; If[PrimeQ[c], AppendTo[a, c]], {x, 0, 100}]; a - Artur Jasinski (grafix(AT)csl.pl), Feb 09 2007

Cf. A107036 = indices of prime Jacobsthal numbers.

Cf. A000979, A124400, A124401, A127955, A127956, A127957, A127958, A127936.

Sequence in context: A139758 A060770 A120334 this_sequence A128925 A158361 A131261

Adjacent sequences: A000975 A000976 A000977 this_sequence A000979 A000980 A000981

hard,nonn,nice

N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)

a(30) from Kamil Duszenko (kdusz(AT)wp.pl), Feb 03 2003

a(31) through a(39) from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 11 2005

No other terms below 720000

a(30) has been proved prime by Francois Morain, thanks to FastECPP. - Tony Reix (tony.reix(AT)laposte.net), Sep 03 2007

a(40) from Alexander Adamchuk (alex(AT)kolmogorov.com), Jun 19 2008