login
A089682
Primes of the form 3*m^2 - 1.
7
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
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: A376910 A142346 A106980 * A211671 A374179 A198693
KEYWORD
nonn,easy
AUTHOR
Giovanni Teofilatto, Jan 05 2004
EXTENSIONS
More terms from Rick L. Shepherd, May 18 2005
STATUS
approved