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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 Pierre CAMI, Table of n, a(n) for n = 0..2300 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. A040040, A045753, A002822, A124065, A124518-A124522. Cf. A071256, A060210, A060256. For records see A125848, A125019. Cf. A076806 (requires odd k) Sequence in context: A183157 A211957 A338397 * A367178 A259985 A144084 Adjacent sequences: A063980 A063981 A063982 * A063984 A063985 A063986 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.)