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

1,1

Links

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

Formula

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

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 *)

Prog

(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
(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
(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

Crossrefs

Cf. A000045, A001690.

Sequence in context: A347154 A009860 A294249 * A213398 A002442 A350143

Adjacent sequences: A138102 A138103 A138104 * A138106 A138107 A138108

Keyword

easy,nonn

Author

Jonathan Vos Post, May 03 2008

Status

approved