A138105 Partial sums of non-Fibonacci numbers A001690.

4, 10, 17, 26, 36, 47, 59, 73, 88, 104, 121, 139, 158, 178, 200, 223, 247, 272, 298, 325, 353, 382, 412, 443, 475, 508, 543, 579, 616, 654, 693, 733, 774, 816, 859, 903, 948, 994, 1041, 1089, 1138, 1188, 1239, 1291, 1344, 1398, 1454, 1511, 1569, 1628

Offset: 1

Author

Jonathan Vos Post, May 03 2008

Keywords

• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000045, A001690.

Programs

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

Mathematica

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

PARI

phi = (1 + sqrt(5))/2;
a(n) = sum(j=2,n, floor(j +log(sqrt(5)*(log(sqrt(5)*j)/log(phi) + j) -5 +3/j)/log(phi)) - 2);
vector(60, n, n++; a(n)) \\ G. C. Greubel, May 26 2019

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

Formula

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