The On-Line Encyclopedia of Integer Sequences (OEIS)

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A072523

Sum of remainders when n-th Fibonacci number is divided by all smaller Fibonacci numbers > 1.
(history; published version)

#11 by Giovanni Resta at Sat May 06 08:43:33 EDT 2017

STATUS

editing

approved

#10 by Giovanni Resta at Sat May 06 08:42:57 EDT 2017

LINKS

Giovanni Resta, <a href="/A072523/b072523.txt">Table of n, a(n) for n = 1..1000</a>

STATUS

approved

editing

#9 by Harvey P. Dale at Wed Mar 18 15:47:59 EDT 2015

STATUS

editing

approved

#8 by Harvey P. Dale at Wed Mar 18 15:47:55 EDT 2015

MATHEMATICA

Table[Total[Mod[Fibonacci[n], Fibonacci[Range[n-1]]]], {n, 40}] (* Harvey P. Dale, Mar 18 2015 *)

STATUS

approved

editing

#7 by N. J. A. Sloane at Thu Dec 05 19:55:21 EST 2013

AUTHOR

_Amarnath Murthy (amarnath_murthy(AT)yahoo.com), _, Jul 31 2002

Discussion

Thu Dec 05

19:55

OEIS Server: https://oeis.org/edit/global/2075

#6 by Russ Cox at Sat Mar 31 14:11:10 EDT 2012

FORMULA

Conjecture: lim n->inf F(n)/a(n) = sqrt(5)/2 where F(n) is the n-th Fibonacci number and therefore lim n->inf a(n)/a(n-1) = Phi (i.e. (sqrt(5)+1)/2 or lim n->inf F(n)/F(n-1)) - Gerald McGarvey (_Gerald. McGarvey(AT)comcast.net), _, Jul 14 2004

Discussion

Sat Mar 31

14:11

OEIS Server: https://oeis.org/edit/global/929

#5 by Russ Cox at Fri Mar 30 17:27:38 EDT 2012

EXTENSIONS

Edited and extended by _Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), _, Aug 02 2002

Discussion

Fri Mar 30

17:27

OEIS Server: https://oeis.org/edit/global/145

#4 by N. J. A. Sloane at Tue Jul 19 03:00:00 EDT 2005

FORMULA

Conjecture: lim n->inf F(n)/a(n) = sqrt(5)/2 where F(n) is the nth n-th Fibonacci number and therefore lim n->inf a(n)/a(n-1) = Phi (i.e. (sqrt(5)+1)/2 or lim n->inf F(n)/F(n-1)) - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Jul 14 2004

KEYWORD

nonn,new

nonn

#3 by N. J. A. Sloane at Wed Sep 22 03:00:00 EDT 2004

FORMULA

Conjecture: lim n->inf F(n)/a(n) = sqrt(5)/2 where F(n) is the nth Fibonacci number and therefore lim n->inf a(n)/a(n-1) = Phi (i.e. (sqrt(5)+1)/2 or lim n->inf F(n)/F(n-1)) - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Jul 14 2004

KEYWORD

nonn,new

nonn

#2 by N. J. A. Sloane at Thu Feb 19 03:00:00 EST 2004

PROG

(PARI) for(n=1, 38, s=0; for(j=3, n-1, s=s+fibonacci(n)%fibonacci(j)); print1(s, ", "))

KEYWORD

nonn,new

nonn