This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A115051 #29 Jun 15 2025 09:01:19
%S A115051 0,0,1,1,1,3,4,5,4,4,6,15,4,9,3,8,22,42,61
%N A115051 Number of distinct prime factors of F(n + L(n)) where F(n) is the Fibonacci number and L(n) is the Lucas number.
%C A115051 Added a(13)=9 from F(534) and a(14)=3 from F(857) using Kelly's factorizations. a(15)>=5 via F(1379) and a(16)=22 via F(2223). - _R. J. Mathar_, Apr 23 2006
%C A115051 a(19) >= 24. - _Amiram Eldar_, Feb 12 2020
%H A115051 Blair Kelley, <a href="http://mersennus.net/fibonacci//">Factorizations</a>
%H A115051 FactorDB, <a href="http://factordb.com/index.php?query=I9368">Status of F(9368)</a>.
%e A115051 The first three terms are 1 since:
%e A115051 F(2 + L(2)) = 5 (a prime)
%e A115051 F(3 + L(3)) = 13 (a prime)
%e A115051 F(4 + L(4)) = 89 (a prime)
%p A115051 lucas := proc(n::integer) if n = 0 then RETURN(2) ; elif n = 1 then RETURN(1) ; else RETURN(combinat[fibonacci](n-1)+combinat[fibonacci](n+1)) ; fi ; end : for n from 2 to 100 do print(n+lucas(n),"...") ; tst := combinat[fibonacci](n+lucas(n)) ; an := nops(op(2,ifactors(tst))) ; print(an) ; od : # _R. J. Mathar_, Apr 23 2006
%t A115051 Table[PrimeNu[Fibonacci[n+LucasL[n]]],{n,0,15}] (* _Harvey P. Dale_, Nov 12 2016 *)
%Y A115051 Subsequence of A022307.
%Y A115051 Cf. A000045, A000032.
%K A115051 nonn,more
%O A115051 0,6
%A A115051 _Parthasarathy Nambi_, Feb 28 2006
%E A115051 More terms from _R. J. Mathar_, Apr 23 2006
%E A115051 Offset corrected and a(15)-a(18) added from factordb.com by _Amiram Eldar_, Feb 12 2020
%E A115051 a(0)=a(1)=0 inserted by _Max Alekseyev_, Jun 15 2025