A063983 Least k such that k*2^n +/- 1 are twin primes.

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

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