

A122834


Primes in the new Mersenne conjecture; odd primes of the form 2^k+1 or 4^k+3.


4



3, 5, 7, 13, 17, 19, 31, 61, 67, 127, 257, 1021, 4093, 4099, 8191, 16381, 65537, 65539, 131071, 262147, 524287, 1048573, 4194301, 16777213, 268435459, 1073741827, 2147483647, 2305843009213693951, 19342813113834066795298819
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Let p be a prime in this sequence. Call q=2^p1 and r=(2^p+1)/3. The new Mersenne conjecture implies that either q and r are both prime or both composite.


LINKS

Gord Palameta, Table of n, a(n) for n = 1..40
P. T. Bateman, J. L. Selfridge and S. S. Wagstaff, Jr., The New Mersenne Conjecture, Amer. Math. Monthly 96, 125128, 1989.
John Renze and Eric Weisstein's World of Mathematics, MathWorld: New Mersenne Prime Conjecture


MATHEMATICA

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]]


CROSSREFS

Superset of: A000668, A019434, A228026.
Cf. A000043 (n such that 2^n1 is prime), A000978 (n such that (2^n+1)/3 is prime), A107360 (the intersection of these).
Sequence in context: A155045 A144296 A045399 * A174265 A107360 A058341
Adjacent sequences: A122831 A122832 A122833 * A122835 A122836 A122837


KEYWORD

nonn


AUTHOR

T. D. Noe, Sep 12 2006


STATUS

approved



