A120393 Sequence a(n) defined as follows: let p(0) = 2 be the first prime; then p(n+1) = least prime of the form a(n)*p(n)*(a(n)*p(n)+1)-1.

1, 1, 5, 1, 14, 5, 86, 130, 139, 54, 1227, 2676, 5709, 5885

Offset

1,3

Comments

The p(n) sequence starts 5, 29, 21169, 448147729, ...

Links

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

Example

1*2*(1*2+1)-1 = 5 is prime, so a(1) = 1.
1*5*(1*5+1)-1 = 29 is prime, so a(2) = 1.

Mathematica

f[0] = {0, 2}; 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. A120392, A120394, A120395, A120396, A143181.

Sequence in context: A270654 A067558 A104792 * A370518 A094368 A295574

Adjacent sequences: A120390 A120391 A120392 * A120394 A120395 A120396

Keyword

nonn

Author

Pierre CAMI, Jul 01 2006, Jul 28 2008

Extensions

Edited by N. J. A. Sloane, Aug 13 2008 at the suggestion of R. J. Mathar

a(12)-a(14) from Amiram Eldar, Aug 28 2021

Status

approved