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%I #25 Mar 06 2023 16:56:02
%S 3,7,8,25,146,169,182,751,812,1507,1591,3157,3752,10651,12740,71804,
%T 155953
%N Indices of prime Fibonacci 5-step numbers, A001591.
%C No other n < 44000.
%C The Noe and Post reference below utilizes a scheme for its indices which differs by 3 from the indices in A001591. - _Robert Price_, Oct 13 2014
%C The sequence is similar to A248757 which uses the indexing scheme starting at 0 as defined by A001591. - _Robert Price_, Oct 13 2014
%C a(18) > 2*10^5. - _Robert Price_, Oct 13 2014
%H Tony D. Noe and Jonathan Vos Post, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL8/Noe/noe5.html">Primes in Fibonacci n-step and Lucas n-step Sequences,</a> J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step Number</a>
%t a = {1, 0, 0, 0, 0}; lst = {}; Do[s = Plus @@ a; a = RotateLeft[a];
%t a[[-1]] = s; If[PrimeQ[s], AppendTo[lst, n]], {n, 44000}]; lst
%t Flatten[Position[LinearRecurrence[{1,1,1,1,1},{0,0,0,0,1},13000],_?PrimeQ]]-4 (* _Harvey P. Dale_, Mar 06 2023 *)
%Y Cf. A105757 (prime Fibonacci 5-step numbers).
%K nonn
%O 1,1
%A _T. D. Noe_, Apr 22 2005
%E Restored original sequence after reconsideration and added a(16)-a(17) by _Robert Price_, Oct 13 2014