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A002234 Numbers k such that the Woodall number k*2^k - 1 is prime.

%I A002234 M0820 N0311 #73 Apr 25 2025 10:28:17
%S A002234 2,3,6,30,75,81,115,123,249,362,384,462,512,751,822,5312,7755,9531,
%T A002234 12379,15822,18885,22971,23005,98726,143018,151023,667071,1195203,
%U A002234 1268979,1467763,2013992,2367906,3752948,17016602
%N A002234 Numbers k such that the Woodall number k*2^k - 1 is prime.
%C A002234 a(34) = 17016602 is tentative until the range 16838832..17016601 is fully searched. - _Eric W. Weisstein_, Mar 22 2018
%D A002234 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 115, p. 40, Ellipses, Paris 2008.
%D A002234 R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section B20.
%D A002234 F. Le Lionnais, Les Nombres Remarquables, Paris, Hermann, 1983, p. 95, 1983.
%D A002234 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 241-242.
%D A002234 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002234 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A002234 David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 139.
%H A002234 Ray Ballinger, <a href="http://web.archive.org/web/20161028080439/http://www.prothsearch.net/woodall.html">Woodall Primes: Definition and Status</a>.
%H A002234 Ray Ballinger and Wilfrid Keller, <a href="http://web.archive.org/web/20161028080439/http://www.prothsearch.net/woodall.html">Woodall numbers</a>.
%H A002234 C. K. Caldwell, <a href="https://t5k.org/glossary/page.php?sort=WoodallNumber">Woodall Numbers</a>.
%H A002234 J. DeMaio, <a href="http://web.archive.org/web/20060125024204/http://science.kennesaw.edu/~jdemaio/generali.htm">Generalized Woodall Numbers</a>.
%H A002234 Brady Haran and Matt Parker, <a href="https://www.youtube.com/watch?v=PQDvEJFdY1U">383 is cool</a>, Numberphile video (2017).
%H A002234 R. Ondrejka, <a href="http://www.utm.edu/research/primes/lists/top_ten/">The Top Ten: a Catalogue of Primal Configurations</a>.
%H A002234 PrimeGrid, <a href="http://www.primegrid.com/primes/primes.php?project=WOO">PrimeGrid Primes: Subproject: (WOO) Woodall Prime Search</a>.
%H A002234 Matt Parker and Brady Haran, <a href="https://www.youtube.com/watch?v=PQDvEJFdY1U">383 and Woodall Primes</a>, Numberphile video (2017).
%H A002234 H. Riesel, <a href="http://dx.doi.org/10.1090/S0025-5718-1969-0262163-1">Lucasian criteria for the primality of N=h.2^n-1</a>, Math. Comp., 23 (1969), 869-875.
%H A002234 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WoodallNumber.html">Woodall Number</a>.
%H A002234 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>.
%o A002234 (PARI) is(n)=isprime(n<<n - 1) \\ _Charles R Greathouse IV_, Feb 07 2017
%Y A002234 Cf. A050918 (for the actual primes), A003261, A005849.
%K A002234 nonn,nice,hard
%O A002234 1,1
%A A002234 _N. J. A. Sloane_, _Simon Plouffe_
%E A002234 a(27) communicated by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 15 2004
%E A002234 a(28) = 1195203 found by M. Rodenkirch; contributed by _Eric W. Weisstein_, Nov 29 2005
%E A002234 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008
%E A002234 a(30)-a(33) from _John Blazek_, May 14 2009
%E A002234 a(34) = 17016602 communicated by _Eric W. Weisstein_, Mar 22 2018