A163154 Primes one less than a Golden rectangle number.

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

Offset

1,1

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

Links

Table of n, a(n) for n=1..8.

Example

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

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 *)

Prog

(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 */

Crossrefs

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

Sequence in context: A172116 A007619 A163212 * A354157 A165387 A361138

Adjacent sequences: A163151 A163152 A163153 * A163155 A163156 A163157

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jul 21 2009

Extensions

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

a(8) from Colin Barker, Apr 07 2016

Status

approved