A104523 Numbers that are neither Fibonacci nor Lucas numbers.

6, 9, 10, 12, 14, 15, 16, 17, 19, 20, 22, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86

Offset: 1

Author

Ido Romano (idoromano(AT)gmail.com), Apr 20 2005

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000032, A000045.

Intersection of A001690 and A090946.

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 : islucas := proc(i::integer) local lucn,n ; for n from 0 to i do lucn := lucas(n) ; if lucn = i then RETURN(1) ; elif lucn > i then RETURN(0) ; fi ; od : end : isfibo := proc(i::integer) local fibn,n ; for n from 0 to i+1 do fibn := combinat[fibonacci](n) ; if fibn = i then RETURN(1) ; elif fibn > i then RETURN(0) ; fi ; od : end : for n from 0 to 100 do if islucas(n) = 0 and isfibo(n) = 0 then printf("%d,",n) ; fi ; od : # R. J. Mathar, Apr 23 2006

Mathematica

a := {1, 3}; For[n = 3, n <= 100, n++,a=Append[a,a[[n-1]]+a[[n-2]]]]; Complement[Range[150], a, Table[Fibonacci[n], {n, 1, 100}]] (* Stefan Steinerberger, Apr 17 2006 *)
Module[{nn=12,fib,luc},fib=Fibonacci[Range[nn]];luc=LucasL[Range[nn]];Complement[ Range[fib[[-1]]],luc,fib]] (* Harvey P. Dale, Mar 10 2019 *)

Extensions

More terms from Stefan Steinerberger and Atilla Bora (borabanana(AT)gmail.com), Apr 17 2006