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Search: id:A063983
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| A063983 |
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Least k such that k*2^n +/- 1 are twin primes. |
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+0
19
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| 4, 2, 1, 9, 12, 6, 3, 9, 57, 30, 15, 99, 165, 90, 45, 24, 12, 6, 3, 69, 132, 66, 33, 486, 243, 324, 162, 81, 90, 45, 345, 681, 585, 375, 267, 426, 213, 429, 288, 144, 72, 36, 18, 9, 147, 810, 405, 354, 177, 1854, 927, 1125, 1197, 666, 333, 519, 1032, 516, 258, 129, 72
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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Richard Crandall and Carl Pomerance, 'Prime Numbers: A Computational Perspective,' Springer-Verlag, NY, 2001, page 12.
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EXAMPLE
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a(3) = 9 because 9*2^3=72, and 71 and 73 are twin primes.
n=6: a(6)=3, 64.3=192 and {191,193} are both primes; n=71: a(71)=630, 630*[2^71]=1487545442103938242314240 and {1487545442103938242314239, 1487545442103938242314241} are twin primes.
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MATHEMATICA
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Table[Do[s=(2^j)*k; If[PrimeQ[s-1]&&PrimeQ[s+1], Print[{j, k]], {k, 1, 2*j^2], {j, 0, 100]; (*outprint of a[j]=k*)
Do[ k = 1; While[ ! PrimeQ[ k*2^n + 1 ] || ! PrimeQ[ k*2^n - 1 ], k++ ]; Print[ k ], {n, 0, 50} ]
f[n_] := Block[{k = 1}, While[Nand @@ PrimeQ[{-1, 1} + 2^n*k], k++ ]; k]; Table[f[n], {n, 60}] (*Chandler*)
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CROSSREFS
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Cf. A040040, A045753, A002822, A124065, A124518-A124522.
Cf. A071256, A060210, A060256. For records see A125848, A125019.
Adjacent sequences: A063980 A063981 A063982 this_sequence A063984 A063985 A063986
Sequence in context: A021241 A016691 A101020 this_sequence A021010 A075397 A049429
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 06 2001
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EXTENSIONS
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More terms from Labos E. (labos(AT)ana.sote.hu), May 24 2002
Edited by njas, Jul 03 2008 at the suggestion of R. J. Mathar
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