A120392 a(1) is the least k such that p(1) = (k*3)^2 + k*3 - 1 is prime, then a(n+1) is the least k such that (k*p(n))^2 + k*p(n) - 1 = p(n+1) is prime.

1, 1, 1, 1, 13, 1, 101, 130, 109, 418, 388, 876, 5011, 11529

Offset

1,5

Comments

The p(n) sequence starts 11, 131, 17291, 298995971, 15108361827832297751, ...

Links

Table of n, a(n) for n=1..14.

Example

a(1) = 1 as 3^2 + 3 - 1 = 11 = p(1) is prime.

Mathematica

f[0] = {0, 3}; f[n_] := f[n] = Module[{k = 1, p = f[n - 1][[2]]}, While[! PrimeQ[(k*p)^2 + k*p - 1], k++]; {k, (k*p)^2 + k*p - 1}]; Table[f[n][[1]], {n, 1, 10}] (* Amiram Eldar, Aug 28 2021 *)

Crossrefs

Cf. A120393, A120394, A120395, A120396.

Sequence in context: A278345 A277866 A278594 * A133371 A223515 A281092

Adjacent sequences: A120389 A120390 A120391 * A120393 A120394 A120395

Keyword

nonn

Author

Pierre CAMI, Jul 01 2006

Extensions

a(11)-a(14) from Amiram Eldar, Aug 28 2021

Status

approved