

A122834


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


1



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
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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.


REFERENCES

P. T. Bateman, J. L. Selfridge, S. S. Wagstaff, Jr., The new Mersenne conjecture, Amer. Math. Monthly, 96 (1989), 125128.


LINKS

Table of n, a(n) for n=1..29.
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

Cf. A000043 (n such that 2^n1 is prime), A000978 (n such that (2^n+1)/3 is prime).
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



