OFFSET
1,2
COMMENTS
The respective period lengths of S(n) are given by A001175(n-1) (which is the Pisano period to n-1) for n>=2.
The inequality a(n)<=2n-3 holds for n>2.
a(n)=2n-3 infinitely often; lim sup a(n)/n=2 for n-->oo.
EXAMPLE
a(3)=3, since the digital sum analog base 3 of the Fibonacci sequence is S(3)=0,1,1,2,3,3,2,3,3,... where the pattern {2,3,3} is the periodic part (see A131294) and so has a maximal value of 3.
a(9)=13 because the pattern base 9 is {2,3,5,8,13,13,10,7,9,8,9,9} (see A010076) where the maximal value is 13.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Hieronymus Fischer, Jul 08 2007
STATUS
approved