A110849 - OEIS

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

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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 A378509 A127663

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