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 A163154 Primes one less than a Golden rectangle number. 3
 5, 103, 3478759199, 116139356908771351, 37396512239913013823, 285687842248637730909432643746211633, 1391541769353191693086710038712557510379751, 1550980526109101915069808788349000570735950731617761605783 (list; graph; refs; listen; history; text; internal format)
 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 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 * A165387 A156848 A057016 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

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Last modified January 19 13:17 EST 2021. Contains 340270 sequences. (Running on oeis4.)