A059248 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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