|
%I #18 Nov 14 2018 01:49:27
%S 3,5,7,13,17,19,31,61,67,127,257,1021,4093,4099,8191,16381,65537,
%T 65539,131071,262147,524287,1048573,4194301,16777213,268435459,
%U 1073741827,2147483647,2305843009213693951,19342813113834066795298819
%N Primes in the new Mersenne conjecture; odd primes of the form 2^k+-1 or 4^k+-3.
%C Let p be a prime in this sequence. Call q=2^p-1 and r=(2^p+1)/3. The new Mersenne conjecture implies that either q and r are both prime or both composite.
%H Gord Palameta, <a href="/A122834/b122834.txt">Table of n, a(n) for n = 1..40</a>
%H P. T. Bateman, J. L. Selfridge and S. S. Wagstaff, Jr., <a href="http://www.jstor.org/stable/2323195">The New Mersenne Conjecture</a>, Amer. Math. Monthly 96, 125-128, 1989.
%H John Renze and Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NewMersennePrimeConjecture.html">MathWorld: New Mersenne Prime Conjecture</a>
%t nn=100; Union[Select[1+2^Range[16],PrimeQ], Select[ -1+2^Range[2nn],PrimeQ], Select[3+4^Range[nn],PrimeQ], Select[ -3+4^Range[nn],PrimeQ]]
%Y Superset of: A000668, A019434, A228026.
%Y Cf. A000043 (n such that 2^n-1 is prime), A000978 (n such that (2^n+1)/3 is prime), A107360 (the intersection of these).
%K nonn
%O 1,1
%A _T. D. Noe_, Sep 12 2006
|
