A163157 Primes of the form 1 + some Golden Rectangle Number.

2, 3, 7, 41, 1871, 4599466948725481982057, 153554501132879618787551305057

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 21 2009

Keywords

• nonn

Comments

Primes of the form 1+A001654(k) for some k, as actually generated by k=1, 2, 3, 5, 9, 53, 71,....

Also primes of the form Fibonacci(k)*Fibonacci(k+1)+1. - Colin Barker, Apr 08 2016

The next term (a(8)) has 1995 digits. - Harvey P. Dale, May 15 2018

Crossrefs

Cf. A001654, A000045, A163154, A163155, A163156.

Programs

Mathematica

q=0;lst={};Do[f=Fibonacci[n];If[PrimeQ[f*q+1],AppendTo[lst,f*q+1]];q=f, {n,3*6!}];lst
Select[Times@@@Partition[Fibonacci[Range[100]],2,1]+1,PrimeQ] (* Harvey P. Dale, May 15 2018 *)

PARI

for(k=1, 1000, if(isprime(p=fibonacci(k)*fibonacci(k+1)+1), print1(p, ","))) \\ Colin Barker, Apr 08 2016

Extensions

Slightly edited by R. J. Mathar, Jul 25 2009