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Prime numbers of the form (2^k + k^2)/3.
1

%I #28 Mar 07 2020 04:06:28

%S 19,59,43787,11185019,2932031008019,768614336404565891,

%T 3148244321913096810907,

%U 1177898043185589553055531667161945677218322597917079305414404134195099211

%N Prime numbers of the form (2^k + k^2)/3.

%C The corresponding values of k are 5, 7, 17, 25, 43, 61, 73, 241, 739, 833, 1297, 1981, 4211, 4501, 7739, 8141, 24965, ... - _Amiram Eldar_, Mar 07 2020

%H Amiram Eldar, <a href="/A270818/b270818.txt">Table of n, a(n) for n = 1..12</a>

%H José Camacho Medina's Matematico Fresnillense, <a href="http://matematicofresnillense.blogspot.mx/2011/09/nueva-formula-generadora-de-numeros.html">Nueva Fórmula Generadora de Números Primos: Función Camila (in Spanish)</a>.

%t Select[Table[(2^n + n^2)/3, {n, 1, 1000}], PrimeQ]

%o (PARI) forstep(n=5,1e3,[2,4], if(isprime(t=(2^n+n^2)/3), print1(t", "))) \\ _Charles R Greathouse IV_, Apr 07 2016

%Y Cf. A000043, A057468.

%K nonn

%O 1,1

%A _José de Jesús Camacho Medina_, Apr 07 2016