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A063983 Least k such that k*2^n +/- 1 are twin primes. 20
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; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Excluding the first three terms, all remaining terms have digital root 3, 6, or 9. - J. W. Helkenberg, Jul 24 2013
REFERENCES
Richard Crandall and Carl Pomerance, 'Prime Numbers: A Computational Perspective,' Springer-Verlag, NY, 2001, page 12.
LINKS
EXAMPLE
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.
MATHEMATICA
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}] (* Ray Chandler, Jan 09 2009 *)
CROSSREFS
Cf. A071256, A060210, A060256. For records see A125848, A125019.
Cf. A076806 (requires odd k)
Sequence in context: A183157 A211957 A338397 * A367178 A259985 A144084
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Sep 06 2001
EXTENSIONS
More terms from Labos Elemer, May 24 2002
Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar
STATUS
approved

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Last modified June 15 06:51 EDT 2024. Contains 373402 sequences. (Running on oeis4.)