A110849 Consider the sequence b(0)=127 and for n>0, b(n) is the least prime of the form k * b(n-1)^2 - 1 where k is a multiple of 6. This sequence gives the values of k.

30, 42, 30, 84, 516, 768, 804, 4806, 2838, 174, 23418, 22770

Offset

1,1

Links

Table of n, a(n) for n=1..12.

Example

127,
30*127^2-1,
42*(30*127^2-1)^2-1,
30*(42*(30*127^2-1)^2-1)^2-1,
84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1,
516*(84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1)^2-1,
768*(516*(84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1)^2-1)^2-1,
804*(768*(516*(84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1,
4806*(804*(768*(516*(84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1,
2838*(4806*(804*(768*(516*(84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1,
174*(2838*(4806*(804*(768*(516*(84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1,
23418*(174*(2838*(4806*(804*(768*(516*(84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1,
and 22770*(23418*(174*(2838*(4806*(804*(768*(516*(84*(30*(42*(30*127^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1)^2-1,
are primes.

Mathematica

lpf[{n_, t_}]:=Module[{a=t^2, k=6}, While[!PrimeQ[k*a-1], k=k+6]; {k, k*a-1}]; Rest[ NestList[lpf, {127, 127}, 12][[All, 1]]] (* Harvey P. Dale, Apr 25 2017 *)

Crossrefs

Sequence in context: A039297 A043900 A103098 * A074696 A127663 A008885

Adjacent sequences: A110846 A110847 A110848 * A110850 A110851 A110852

Keyword

nonn,more

Author

Pierre CAMI, Sep 17 2005

Extensions

Edited by Ray Chandler, Sep 26 2005

Definition amended by Georg Fischer, Jun 18 2021

Status

approved