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

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

Offset

1,1

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

Links

Table of n, a(n) for n=1..7.

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 *)

Prog

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

Crossrefs

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

Sequence in context: A102604 A119662 A265776 * A260819 A000945 A261564

Adjacent sequences: A163154 A163155 A163156 * A163158 A163159 A163160

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 21 2009

Extensions

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

Status

approved