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Search: id:A122834
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| A122834 |
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Primes in the new Mersenne conjecture; odd primes of the form 2^k+-1 or 4^k+-3. |
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+0
2
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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.
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REFERENCES
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P. T. Bateman, J. L. Selfridge, S. S. Wagstaff, Jr., The new Mersenne conjecture, Amer. Math. Monthly, 96 (1989), 125-128.
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LINKS
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John Renze and Eric Weisstein's World of Mathematics, MathWorld: New Mersenne Prime Conjecture
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MATHEMATICA
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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]]
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CROSSREFS
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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 this_sequence A107360 A058341 A116036
Adjacent sequences: A122831 A122832 A122833 this_sequence A122835 A122836 A122837
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Sep 12 2006
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