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%I #8 Sep 08 2022 08:44:39
%S 2,3,4,7,14,25,45,78,132,219,362,594,970,1579,2565,4161,6743,10923,
%T 17687,28632,46342,74998,121365,196389,317781,514198,832008,1346236,
%U 2178274,3524542,5702850,9227427,14930313,24157777,39088128,63245944,102334112,165580097,267914251,433494391
%N 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( ).
%H G. C. Greubel, <a href="/A014251/b014251.txt">Table of n, a(n) for n = 1..1000</a>
%t 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 *)
%o (PARI) lgg(x)=log(x)/log((sqrt(5)+1)/2);
%o c(n)=floor(n+lgg(sqrt(5)*(lgg(sqrt(5)*n)+n)-5+3/n)-2);
%o 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
%o (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
%o (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
%K nonn
%O 1,1
%A _Clark Kimberling_
%E Terms a(33) onward added by _G. C. Greubel_, Jun 18 2019
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