cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A125019 Records in A063983 if the initial 4 is ignored (cf. A125848).

Original entry on oeis.org

2, 9, 12, 57, 99, 165, 486, 681, 810, 1854
Offset: 1

Views

Author

Artur Jasinski, Nov 16 2006

Keywords

Crossrefs

Extensions

Corrected and extended by R. J. Mathar, Nov 29 2006

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

Original entry on oeis.org

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

Views

Author

Robert G. Wilson v, Sep 06 2001

Keywords

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.

Crossrefs

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
Showing 1-2 of 2 results.