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

%I A096362 #28 Jan 08 2020 10:35:10
%S A096362 2,3,7,11,29,47,19,41,199,23,521,281,31,2207,3571,107,9349,2161,211,
%T A096362 43,307,139,461,1103,101,151,90481,5779,14503,59,19489,2521,3010349,
%U A096362 1087,4481,9901,67,63443,71,911,103681,54018521,29134601,79,859,1601,3041
%N A096362 Order in which prime factors first occur in the Lucas sequence.
%H A096362 Metin Sariyar, <a href="/A096362/b096362.txt">Table of n, a(n) for n = 1..750</a>
%H A096362 J. Brillhart, P. L. Montgomery and R. D. Silverman, <a href="https://doi.org/10.1090/S0025-5718-1988-0917832-6">Tables of Fibonacci and Lucas factorizations</a>, Math. Comp. 50 (1988), 251-260, S1-S15. Math. Rev. 89h:11002.
%H A096362 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/lucas200.html">The First 200 Lucas numbers and their factors</a>
%H A096362 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/matha1/matha113.htm">Lucas numbers (n=1 to 100)</a>
%p A096362 L:= gfun:-rectoproc({a(n)=a(n-1)+a(n-2),a(0)=2,a(1)=1},a(n),remember):
%p A096362 S:= {}: Res:= NULL:
%p A096362 for n from 0 to 100 do
%p A096362   P:= numtheory:-factorset(L(n)) minus S;
%p A096362   Res:= Res, op(sort(convert(P,list)));
%p A096362   S:= S union P;
%p A096362 od:
%p A096362 Res; # _Robert Israel_, Jan 06 2020
%t A096362 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 *)
%t A096362 Drop[DeleteDuplicates[Flatten[Table[First/@FactorInteger[LucasL[n]],{n,0,100}]]],{2}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 05 2012 *)
%Y A096362 Cf. A000032.
%K A096362 nonn
%O A096362 1,1
%A A096362 _Lekraj Beedassy_, Jun 30 2004
%E A096362 Edited, corrected and extended by _Robert G. Wilson v_, Jul 01 2004