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

Author

Lekraj Beedassy, Jun 30 2004

Keywords

• nonn

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)

Crossrefs

Cf. A000032.

Programs

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 *)

Extensions

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