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A096362 Order in which prime factors first occur in the Lucas sequence. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 18 09:26 EDT 2021. Contains 343995 sequences. (Running on oeis4.)