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Primes of the form 1 + some Golden Rectangle Number.
2

%I #9 May 15 2018 14:45:10

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

%N Primes of the form 1 + some Golden Rectangle Number.

%C Primes of the form 1+A001654(k) for some k, as actually generated by k=1, 2, 3, 5, 9, 53, 71,....

%C Also primes of the form Fibonacci(k)*Fibonacci(k+1)+1. - _Colin Barker_, Apr 08 2016

%C The next term (a(8)) has 1995 digits. - _Harvey P. Dale_, May 15 2018

%t q=0;lst={};Do[f=Fibonacci[n];If[PrimeQ[f*q+1],AppendTo[lst,f*q+1]];q=f, {n,3*6!}];lst

%t Select[Times@@@Partition[Fibonacci[Range[100]],2,1]+1,PrimeQ] (* _Harvey P. Dale_, May 15 2018 *)

%o (PARI) for(k=1, 1000, if(isprime(p=fibonacci(k)*fibonacci(k+1)+1), print1(p, ","))) \\ _Colin Barker_, Apr 08 2016

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

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jul 21 2009

%E Slightly edited by _R. J. Mathar_, Jul 25 2009