A138105 - OEIS

%I #18 Sep 08 2022 08:45:33

%S 4,10,17,26,36,47,59,73,88,104,121,139,158,178,200,223,247,272,298,

%T 325,353,382,412,443,475,508,543,579,616,654,693,733,774,816,859,903,

%U 948,994,1041,1089,1138,1188,1239,1291,1344,1398,1454,1511,1569,1628

%N Partial sums of non-Fibonacci numbers A001690.

%H Harvey P. Dale, <a href="/A138105/b138105.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = Sum_{j=1..n} A001690(j).

%t Module[{nn=100,k},k=Floor[Log[GoldenRatio,nn*Sqrt[5]]];Accumulate[ Complement[ Range[nn],Fibonacci[Range[k]]]]] (* _Harvey P. Dale_, Apr 29 2018 *)

%t Table[Sum[Floor[j +Log[GoldenRatio, Sqrt[5]*(Log[GoldenRatio, Sqrt[5]*j] + j) -5 +3/j] -2], {j,2,n}], {n, 2, 60}] (* _G. C. Greubel_, May 26 2019 *)

%o (PARI) phi = (1 + sqrt(5))/2;

%o a(n) = sum(j=2,n, floor(j +log(sqrt(5)*(log(sqrt(5)*j)/log(phi) + j) -5 +3/j)/log(phi)) - 2);

%o vector(60, n, n++; a(n)) \\ _G. C. Greubel_, May 26 2019

%o (Magma) phi:= (1+Sqrt(5))/2; [(&+[Floor(j + Log(phi, Sqrt(5)*(Log(phi, Sqrt(5)*j) + j) - 5 + 3/j) - 2): j in [2..n]]): n in [2..60]];  // _G. C. Greubel_, May 26 2019

%o (Sage) [sum(floor(j +log(sqrt(5)*(log(sqrt(5)*j, golden_ratio) + j) -5 +3/j, golden_ratio) - 2) for j in (2..n)) for n in (2..60)] # _G. C. Greubel_, May 26 2019

%Y Cf. A000045, A001690.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, May 03 2008