A089682 Primes of the form 3*m^2 - 1.

2, 11, 47, 107, 191, 431, 587, 971, 1451, 2027, 2351, 2699, 3467, 4799, 5807, 6911, 7499, 8111, 8747, 10091, 10799, 14699, 15551, 16427, 17327, 18251, 25391, 27647, 36299, 41771, 44651, 55487, 57131, 62207, 67499, 71147, 74891, 80687, 92927

Offset

1,1

Comments

431 and 27647 also have the form 2*m^3-1 (431 = 3*12^2-1 = 2*6^3-1 and 27647 = 3*96^2-1 = 2*24^3-1). [Howard Berman (howard_berman(AT)hotmail.com), May 09 2009]

Or, primes p such that 3*(p+1) is a square. [Vincenzo Librandi, Nov 18 2010]

Obviously m must be either 1 or an even number. So this consists of 1 together with primes of the form 12*u^2 - 1. - N. J. A. Sloane, Aug 09 2019

References

M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988

Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta, UTET, CittaStudiEdizioni, Milano 1997

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Mathematica

Select[Table[3 n^2 - 1, {n, 0, 2000}], PrimeQ] (* Vincenzo Librandi, Jul 16 2012 *)

Prog

(Magma) [a: n in [0..200] | IsPrime(a) where a is 3*n^2-1]; // Vincenzo Librandi, Jul 16 2012

Crossrefs

Primes in A080663.

Sequence in context: A229019 A142346 A106980 * A211671 A198693 A178710

Adjacent sequences: A089679 A089680 A089681 * A089683 A089684 A089685

Keyword

nonn,easy

Author

Giovanni Teofilatto, Jan 05 2004

Extensions

More terms from Rick L. Shepherd, May 18 2005

Status

approved