A023489 Sum of n-th Lucas number greater than 3 and n-th number that is 1 or is not a Fibonacci number.

5, 11, 17, 25, 38, 57, 87, 135, 213, 337, 537, 860, 1382, 2226, 3591, 5800, 9372, 15151, 24501, 39629, 64106, 103710, 167790, 271473, 439235, 710679, 1149884, 1860533, 3010385, 4870884, 7881234, 12752082, 20633279, 33385323, 54018563, 87403846, 141422368

Offset

1,1

Links

Table of n, a(n) for n=1..37.

Formula

a(n) = phi^(n+2) + n + log_phi(n) + O(1), where phi = 1/2 + sqrt(5)/2 is the golden ratio. - Charles R Greathouse IV, Jan 17 2012

a(n) = A000032(n+2) + A001690(n-1), n >= 2. - R. J. Mathar, Feb 01 2019

Mathematica

nMax = 50; With[{luke = LucasL[Range[3, nMax + 2]], dn = Take[Join[{1}, Complement[Range[2nMax], Fibonacci[Range[2nMax]]]], nMax]}, Total /@ Thread[{luke, nMax}]] (* Harvey P. Dale, Jan 17 2012 *)

Prog

(PARI) b(n)=fibonacci(n+1)+fibonacci(n+3)
d(n)=my(k=2); n-=3; while(fibonacci(k++)<=n+k, ); n+k
a(n)=b(n)+d(n) \\ Charles R Greathouse IV, Jan 17 2012

Crossrefs

Sequence in context: A246296 A368874 A089110 * A268307 A108294 A046869

Adjacent sequences: A023486 A023487 A023488 * A023490 A023491 A023492

Keyword

nonn

Author

Clark Kimberling

Extensions

a(28)-a(37) corrected by Harvey P. Dale, Jan 17 2012

Status

approved