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%I #34 Sep 08 2022 08:45:12
%S 2,11,47,107,191,431,587,971,1451,2027,2351,2699,3467,4799,5807,6911,
%T 7499,8111,8747,10091,10799,14699,15551,16427,17327,18251,25391,27647,
%U 36299,41771,44651,55487,57131,62207,67499,71147,74891,80687,92927
%N Primes of the form 3*m^2 - 1.
%C 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]
%C Or, primes p such that 3*(p+1) is a square. [_Vincenzo Librandi_, Nov 18 2010]
%C 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
%D M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988
%D Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta, UTET, CittaStudiEdizioni, Milano 1997
%H Vincenzo Librandi, <a href="/A089682/b089682.txt">Table of n, a(n) for n = 1..1000</a>
%t Select[Table[3 n^2 - 1, {n, 0, 2000}], PrimeQ] (* _Vincenzo Librandi_, Jul 16 2012 *)
%o (Magma) [a: n in [0..200] | IsPrime(a) where a is 3*n^2-1]; // _Vincenzo Librandi_, Jul 16 2012
%Y Primes in A080663.
%K nonn,easy
%O 1,1
%A _Giovanni Teofilatto_, Jan 05 2004
%E More terms from _Rick L. Shepherd_, May 18 2005
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