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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
OFFSET
1,1
COMMENTS
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.
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, Section A3.
LINKS
P. T. Bateman, J. L. Selfridge, and S. S. Wagstaff, Jr., The New Mersenne Conjecture, Amer. Math. Monthly 96, 125-128, 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^n-1 is prime), A000978 (n such that (2^n+1)/3 is prime), A107360 (the intersection of these).
Sequence in context: A155045 A144296 A045399 * A174265 A346645 A107360
KEYWORD
nonn
AUTHOR
T. D. Noe, Sep 12 2006
STATUS
approved