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A227885 Primes in the union of all n-step Lucas sequences. 2

%I #26 Oct 30 2023 07:27:55

%S 2,3,7,11,29,31,47,71,113,127,131,191,199,223,239,241,367,439,443,521,

%T 863,983,1013,1499,1871,2003,2207,3571,6553,8087,8191,9349,16369,

%U 32647,32707,36319,63487,65407,65519,122401,126719,131071,196331,260111,524287

%N Primes in the union of all n-step Lucas sequences.

%H T. D. Noe, <a href="/A227885/b227885.txt">Table of n, a(n) for n = 1..1000</a> (first 383 terms from Robert Price)

%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

%F 2 and the primes in A127208.

%t plst={2}; plimit=10^39; For[n=2, n<=3+Log[2,plimit], n++, llst={}; For[i=1, i<n, i++, AppendTo[llst,-1]]; AppendTo[llst,n]; For[k=2, k<=2*(1+Log[GoldenRatio, plimit*Sqrt[5]+0.5]), k++, sum=Sum[llst[[j+k-2]], {j,1,n}]; AppendTo[llst,sum]; If[sum<=plimit && PrimeQ[sum], AppendTo[plst,sum]]]]; Union[plst]

%Y Cf. A127208, A000032, A001644, A073817, A074048, A074584, A104621, A105754, A105755.

%K nonn

%O 1,1

%A _Robert Price_, Oct 25 2013

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Last modified March 28 21:57 EDT 2024. Contains 371254 sequences. (Running on oeis4.)