OFFSET
1,5
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..1000
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_, Jul 14 2004
EXAMPLE
The eighth Fibonacci number is 21; division by 2, 3, 5, 8,13 gives the remainders 1, 0, 1, 5, 8, so a(8) = 1 + 0 + 1+ 5 + 8 = 15.
MATHEMATICA
Table[Total[Mod[Fibonacci[n], Fibonacci[Range[n-1]]]], {n, 40}] (* _Harvey P. Dale_, Mar 18 2015 *)
PROG
(PARI) for(n=1, 38, s=0; for(j=3, n-1, s=s+fibonacci(n)%fibonacci(j)); print1(s, ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
_Amarnath Murthy_, Jul 31 2002
EXTENSIONS
Edited and extended by _Klaus Brockhaus_, Aug 02 2002
STATUS
approved