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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( ). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A000690 A049876 A049795 * A290992 A265742 A098010

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

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Last modified August 22 05:00 EDT 2019. Contains 326172 sequences. (Running on oeis4.)