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

Author

Robert G. Wilson v, Sep 06 2001

Keywords

• nonn

Comments

Excluding the first three terms, all remaining terms have digital root 3, 6, or 9. - J. W. Helkenberg, Jul 24 2013

Examples

			a(3) = 9 because 9*2^3 = 72 and 71 and 73 are twin primes.
a(6) = 3 because 3*2^6 = 192 and {191, 193} are twin primes.
a(71) = 630 because 630*2^71 = 1487545442103938242314240 and {1487545442103938242314239, 1487545442103938242314241} are twin primes.
		

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

Crossrefs

Cf. A040040, A045753, A002822, A124065, A124518-A124522.

Cf. A071256, A060210, A060256. For records see A125848, A125019.

Cf. A076806 (requires odd k).

Programs

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, 0, 60}] (* Ray Chandler, Jan 09 2009 *)

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