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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 (list; graph; refs; listen; history; text; internal format)
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

P. T. Bateman, J. L. Selfridge, S. S. Wagstaff, Jr., The new Mersenne conjecture, Amer. Math. Monthly, 96 (1989), 125-128.

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^n-1 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

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Last modified April 19 14:18 EDT 2014. Contains 240760 sequences.