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%I #12 Jul 04 2019 13:48:08
%S 5,103,3478759199,116139356908771351,37396512239913013823,
%T 285687842248637730909432643746211633,
%U 1391541769353191693086710038712557510379751,1550980526109101915069808788349000570735950731617761605783
%N Primes one less than a Golden rectangle number.
%C Primes of the form A001654(k)-1, generated at k = 3, 6, 24, 42, 48, 86, 102, 138, 182,....
%C 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
%e 103 is in the sequence because 103 = 8*13-1 = F(6)*F(7)-1.
%t q=0;lst={};Do[f=Fibonacci[n];If[PrimeQ[f*q-1],AppendTo[lst,f*q-1]];q=f, {n,6!}];lst
%t f[n_] := Fibonacci@ n Fibonacci[n + 1] - 1; f /@ Select[Range@ 180, PrimeQ[f@ #] &] (* _Michael De Vlieger_, Apr 07 2016 *)
%t Select[Times@@@Partition[Fibonacci[Range[150]],2,1]-1,PrimeQ] (* _Harvey P. Dale_, Jul 04 2019 *)
%o (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 */
%Y Cf. A001654, A000045, A119996, A163157, A271428.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jul 21 2009
%E Definition reworded by _R. J. Mathar_, Sep 11 2009
%E a(8) from _Colin Barker_, Apr 07 2016
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