A126906 Smallest k such that 1 + k^(2*n+1) + Sum_{j=1..n} k^(2*j) is prime.

1, 2, 1, 2, 1, 10, 17, 2, 1, 2, 1, 94, 122, 22, 1, 80, 1, 4, 6, 2, 1, 242, 3, 6, 5, 80, 1, 12, 1, 82, 96, 2, 7, 188, 1, 136, 69, 158, 1, 2, 1, 954, 50, 118, 1, 570, 14, 90, 45, 6, 1, 228, 38, 4, 6, 22, 1, 12, 1, 580, 86, 336, 24, 768, 1, 1170, 408, 340, 1, 896

Offset: 1

Author

Artur Jasinski, Dec 31 2006

Keywords

• nonn

Comments

1 is a term if and only if number of terms in polynomial is prime.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..250

Crossrefs

Cf. A124151, A119863, A049407, A124175 A124176 A124177, A124178, A124179, A124180, A124181, A126908-A126916.

Programs

Mathematica

a[n_]: = Module[{k = 1}, While[!PrimeQ[1 + k^(2*n+1) + Sum[k^(2*j), {j, 1, n}]], k++]; k]; Array[a, 30] (* Amiram Eldar, Mar 13 2020 *)

PARI

a(n) = my(k = 1); while(! isprime(1 + k^(2*n+1) + sum(j=1, n, k^(2*j))), k++); k; \\ Michel Marcus, Mar 13 2020

Extensions

More terms from Amiram Eldar, Mar 13 2020