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.

0, 0, 1, 1, 1, 3, 4, 5, 4, 4, 6, 15, 4, 9, 3, 8, 22, 42, 61

Offset: 0

Author

Parthasarathy Nambi, Feb 28 2006

Keywords

• nonn
• more

Comments

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

a(19) >= 24. - Amiram Eldar, Feb 12 2020

Examples

			The first three terms are 1 since:
F(2 + L(2)) = 5 (a prime)
F(3 + L(3)) = 13 (a prime)
F(4 + L(4)) = 89 (a prime)
		

Links

• Blair Kelley, Factorizations
• FactorDB, Status of F(9368).

Crossrefs

Subsequence of A022307.

Cf. A000045, A000032.

Programs

Maple

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

Mathematica

Table[PrimeNu[Fibonacci[n+LucasL[n]]],{n,0,15}] (* Harvey P. Dale, Nov 12 2016 *)

Extensions

More terms from R. J. Mathar, Apr 23 2006

Offset corrected and a(15)-a(18) added from factordb.com by Amiram Eldar, Feb 12 2020

a(0)=a(1)=0 inserted by Max Alekseyev, Jun 15 2025