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Primes in A001644 (the Lucas 3-step numbers).
2

%I #12 Feb 16 2025 08:32:57

%S 3,7,11,71,131,241,443,1499,196331,86992799,541292033,

%T 292997064989357251,129824812729295169371,238785058551151434437,

%U 5026368970977284897651,105803877284856287511991

%N Primes in A001644 (the Lucas 3-step numbers).

%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="https://mathworld.wolfram.com/Lucasn-StepNumber.html">Lucas n-Step Number</a>

%F a(n) = A001644(A104576(n)). - _Arthur O'Dwyer_, Jul 31 2024

%t a={-1, -1, 3}; lst={}; Do[s=Plus@@a; a=RotateLeft[a]; a[[ -1]]=s; If[PrimeQ[s], AppendTo[lst, s]], {n, 1000}]; lst

%Y Cf. A104576 (indices of prime Lucas 3-step numbers).

%K nonn,changed

%O 1,1

%A _T. D. Noe_, Apr 22 2005

%E Name clarified by _Arthur O'Dwyer_, Jul 31 2024