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A138105 Partial sums of non-Fibonacci numbers A001690. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A301288 A009860 A294249 * A213398 A002442 A301253

Adjacent sequences:  A138102 A138103 A138104 * A138106 A138107 A138108

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, May 03 2008

STATUS

approved

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Last modified October 14 15:03 EDT 2019. Contains 328019 sequences. (Running on oeis4.)