A096362 Order in which prime factors first occur in the Lucas sequence.

2, 3, 7, 11, 29, 47, 19, 41, 199, 23, 521, 281, 31, 2207, 3571, 107, 9349, 2161, 211, 43, 307, 139, 461, 1103, 101, 151, 90481, 5779, 14503, 59, 19489, 2521, 3010349, 1087, 4481, 9901, 67, 63443, 71, 911, 103681, 54018521, 29134601, 79, 859, 1601, 3041

Offset

1,1

Links

Metin Sariyar, Table of n, a(n) for n = 1..750

J. Brillhart, P. L. Montgomery and R. D. Silverman, Tables of Fibonacci and Lucas factorizations, Math. Comp. 50 (1988), 251-260, S1-S15. Math. Rev. 89h:11002.

Ron Knott, The First 200 Lucas numbers and their factors

Hisanori Mishima, Lucas numbers (n=1 to 100)

Maple

L:= gfun:-rectoproc({a(n)=a(n-1)+a(n-2), a(0)=2, a(1)=1}, a(n), remember):
S:= {}: Res:= NULL:
for n from 0 to 100 do
  P:= numtheory:-factorset(L(n)) minus S;
  Res:= Res, op(sort(convert(P, list)));
  S:= S union P;
od:
Res; # Robert Israel, Jan 06 2020

Mathematica

PrimeFactors[n_Integer] := Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]; L[n_] := Fibonacci[n - 1] + Fibonacci[n + 1]; pf = {}; f[n_] := Block[{p = PrimeFactors[L[n]]}, l = Length[p]; k = 1; While[k <= l, If[ Position[ pf, p[[k]]] == {}, AppendTo[ pf, p[[k]] ]]; k++ ]]; Do[ f[n], {n, 40}]; pf (* Robert G. Wilson v, Jul 01 2004 *)
Drop[DeleteDuplicates[Flatten[Table[First/@FactorInteger[LucasL[n]], {n, 0, 100}]]], {2}] (* Vladimir Joseph Stephan Orlovsky, Feb 05 2012 *)

Crossrefs

Cf. A000032.

Sequence in context: A112840 A014981 A227885 * A005479 A120856 A138000

Adjacent sequences: A096359 A096360 A096361 * A096363 A096364 A096365

Keyword

nonn

Author

Lekraj Beedassy, Jun 30 2004

Extensions

Edited, corrected and extended by Robert G. Wilson v, Jul 01 2004

Status

approved