A059248 Numerator of 1/F(1) + 1/F(2) + 1/F(3) + ... + 1/F(n), where F(n) is the n-th Fibonacci number (A000045).

1, 2, 5, 17, 91, 379, 5047, 35849, 614893, 6800951, 607326679, 3651532639, 851897554247, 24724573280923, 301787157353771, 14188276949397301, 22662903194758542865, 430644772287132696121, 1800653989272587268758525

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..100

Naim Tuglu, Can Kizilates, Seyhun Kesim, On the Harmonic and Hyperharmonic Fibonacci Numbers, arXiv:1505.04284 [math.NT], 2015 (see Table 1).

Example

a(4) = 17 because 1/F1 + 1/F2 + 1/F3 + 1/F4 = 1 + 1 + 1/2 + 1/3 = 17/6 and the numerator is 17.
1, 2, 5/2, 17/6, 91/30, 379/120, 5047/1560, 35849/10920, 614893/185640, 6800951/2042040, 607326679/181741560, ... = A059248/A035105.

Maple

BB:=n->sum(1/fibonacci(i), i=1..n): a:=n->floor(numer(BB(n))): seq(a(n), n=1..19); # Zerinvary Lajos, Mar 28 2007

Mathematica

Table[ 1 / Fibonacci[n], {n, 1, 19}] // Accumulate // Numerator (* Jean-François Alcover, Mar 07 2013 *)

Prog

(PARI) lista(nn) = s = 0; for (n=1, nn, s += 1/fibonacci(n); print1(numerator(s), ", "); ); \\ Michel Marcus, Nov 28 2014

Crossrefs

Cf. A000045, A035105, Cf. A059246/A059247.

Sequence in context: A245108 A195137 A026822 * A203006 A143878 A081546

Adjacent sequences: A059245 A059246 A059247 * A059249 A059250 A059251

Keyword

nonn,easy,frac

Author

Avi Peretz (njk(AT)netvision.net.il), Jan 22 2001

Extensions

More terms from Naohiro Nomoto, Jun 21 2001

Offset changed to 1 by Michel Marcus, Nov 28 2014

Status

approved