A163154 Primes one less than a Golden rectangle number.

5, 103, 3478759199, 116139356908771351, 37396512239913013823, 285687842248637730909432643746211633, 1391541769353191693086710038712557510379751, 1550980526109101915069808788349000570735950731617761605783

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 21 2009

Keywords

• nonn

Comments

Primes of the form A001654(k)-1, generated at k = 3, 6, 24, 42, 48, 86, 102, 138, 182,....

Yet another way of stating the definition: primes of the form F(k)*F(k+1)-1, where F(k) is the k-th Fibonacci number (A000045). - Colin Barker, Apr 07 2016

Examples

			103 is in the sequence because 103 = 8*13-1 = F(6)*F(7)-1.
		

Crossrefs

Cf. A001654, A000045, A119996, A163157, A271428.

Programs

Mathematica

q=0;lst={};Do[f=Fibonacci[n];If[PrimeQ[f*q-1],AppendTo[lst,f*q-1]];q=f, {n,6!}];lst
f[n_] := Fibonacci@ n Fibonacci[n + 1] - 1; f /@ Select[Range@ 180, PrimeQ[f@ #] &] (* Michael De Vlieger, Apr 07 2016 *)
Select[Times@@@Partition[Fibonacci[Range[150]],2,1]-1,PrimeQ] (* Harvey P. Dale, Jul 04 2019 *)

PARI

L=List(); for(k=1, 200, if(isprime(p=fibonacci(k)*fibonacci(k+1)-1), listput(L, p))); Vec(L) /* Colin Barker, Apr 07 2016 */

Extensions

Definition reworded by R. J. Mathar, Sep 11 2009

a(8) from Colin Barker, Apr 07 2016