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 and n >= 2.

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

Offset

2,4

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

Links

Table of n, a(n) for n=2..18.

Blair Kelley, Factorizations

FactorDB, Status of F(9368).

Example

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)

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, 2, 15}] (* Harvey P. Dale, Nov 12 2016 *)

Crossrefs

Cf. A000045, A000032.

Sequence in context: A014250 A155078 A332420 * A094634 A114545 A309704

Adjacent sequences: A115048 A115049 A115050 * A115052 A115053 A115054

Keyword

nonn,more

Author

Parthasarathy Nambi, Feb 28 2006

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

Status

approved