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

Author

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

Keywords

• nonn
• easy
• frac

Examples

			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.
		

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).

Crossrefs

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

Programs

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 *)

PARI

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

Extensions

More terms from Naohiro Nomoto, Jun 21 2001

Offset changed to 1 by Michel Marcus, Nov 28 2014