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Search: id:A057429
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| A057429 |
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Gaussian-Mersenne primes: numbers n such that (1+i)^n - 1 times its conjugate is prime. |
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+0
7
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| 2, 3, 5, 7, 11, 19, 29, 47, 73, 79, 113, 151, 157, 163, 167, 239, 241, 283, 353, 367, 379, 457, 997, 1367, 3041, 10141, 14699, 27529, 49207, 77291, 85237, 106693, 160423, 203789, 364289, 991961
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Equivalently, numbers n such that (1+i)^n - 1 is a Gaussian prime.
Note that n must be a rational prime. Also note that (1+i)^n+i or (1+i)^n-i is also a Gaussian prime. - T. D. Noe (noe(AT)sspectra.com), Jan 31 2005
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REFERENCES
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Mike Oakes, posting to the Mersenne list, Sep 07 2000.
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LINKS
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C. Caldwell, The largest known primes
Marc Chamberland, Binary BBP-Formulae for Logarithms..., J. Integer Seqs., Vol. 6, 2003.
M. Oakes, A new series of Mersenne-like Gaussian primes
M. Oakes, Posting to the Number Theory list, Dec 27 2005
Index entries for Gaussian integers and primes
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EXAMPLE
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Note that 4 is not in the sequence because (1+i)^4 - 1 = -5, which is an integer prime, but not a Gaussian prime.
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MATHEMATICA
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Do[a = (1 + I)^n - 1; b = a*Conjugate[a]; If[PrimeQ[b], Print[n]], {n, 1, 160426}]
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CROSSREFS
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Cf. A000043, A066408, A007670, A007671, A027206.
Cf. A027206 ((1+i)^n + i is a Gaussian prime), A103329 ((1+i)^n - i is a Gaussian prime).
Sequence in context: A039726 A115617 A003064 this_sequence A065726 A118985 A089769
Adjacent sequences: A057426 A057427 A057428 this_sequence A057430 A057431 A057432
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KEYWORD
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nonn,nice,hard
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 07 2000
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EXTENSIONS
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364289 found by Nicholas Glover on Jun 02 2001 - Mike Oakes (mikeoakes2(AT)aol.com)
Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Aug 14 2002; revised by N. J. A. Sloane (njas(AT)research.att.com), Dec 28 2005
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