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

2, 3, 7, 11, 29, 31, 47, 71, 113, 127, 131, 191, 199, 223, 239, 241, 367, 439, 443, 521, 863, 983, 1013, 1499, 1871, 2003, 2207, 3571, 6553, 8087, 8191, 9349, 16369, 32647, 32707, 36319, 63487, 65407, 65519, 122401, 126719, 131071, 196331, 260111, 524287

Offset

1,1

Links

T. D. Noe, Table of n, a(n) for n = 1..1000 (first 383 terms from Robert Price)

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

Formula

2 and the primes in A127208.

Mathematica

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]

Crossrefs

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

Sequence in context: A143926 A112840 A014981 * A096362 A005479 A120856

Adjacent sequences: A227882 A227883 A227884 * A227886 A227887 A227888

Keyword

nonn

Author

Robert Price, Oct 25 2013

Status

approved