A014251 a(n) = b(n) - c(n) where b(n) is the n-th Fibonacci number greater than 2 and c(n) is the n-th number not in sequence b( ).

2, 3, 4, 7, 14, 25, 45, 78, 132, 219, 362, 594, 970, 1579, 2565, 4161, 6743, 10923, 17687, 28632, 46342, 74998, 121365, 196389, 317781, 514198, 832008, 1346236, 2178274, 3524542, 5702850, 9227427, 14930313, 24157777, 39088128, 63245944, 102334112, 165580097, 267914251, 433494391

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Mathematica

Join[{2, 3}, Table[Fibonacci[n+2] - Floor[n-2 + Log[GoldenRatio, Sqrt[5]*(Log[GoldenRatio, Sqrt[5]*(n-2)] + n-2) -5 +3/(n-2)] -2], {n, 4, 50}]] (* G. C. Greubel, Jun 18 2019 *)

Prog

(PARI) lgg(x)=log(x)/log((sqrt(5)+1)/2);
c(n)=floor(n+lgg(sqrt(5)*(lgg(sqrt(5)*n)+n)-5+3/n)-2);
for(n=2, 50, print1(if(n==2, 2, if(n==3, 3, fibonacci(n+2) - c(n-2))), ", ")) \\ G. C. Greubel, Jun 18 2019
(Magma) phi:= (1+Sqrt(5))/2; [2, 3] cat [Fibonacci(n+2) -Floor(n-2 + Log(phi, Sqrt(5)*(Log(phi, Sqrt(5)*(n-2)) + n-2) - 5 + 3/(n-2)) - 2): n in [4..50]]; // G. C. Greubel, Jun 18 2019
(Sage) [2, 3]+[fibonacci(n+2) -floor(n-2+ log( sqrt(5)*(log(sqrt(5)*(n-2), golden_ratio) +n-2) -5 +3/(n-2), golden_ratio) -2 ) for n in (4..50)] # G. C. Greubel, Jun 18 2019

Crossrefs

Sequence in context: A049876 A049795 A329111 * A290992 A361229 A265742

Adjacent sequences: A014248 A014249 A014250 * A014252 A014253 A014254

Keyword

nonn

Author

Clark Kimberling

Extensions

Terms a(33) onward added by G. C. Greubel, Jun 18 2019

Status

approved