cp's OEIS Frontend

A131319 Maximal value arising in the sequence S(n) representing the digital sum analog base n of the Fibonacci recurrence.

%I A131319 #8 Jul 10 2015 19:58:33
%S A131319 1,2,3,5,5,9,11,13,13,17,19,13,19,25,27,26,25,33,35,32,33,34,35,45,41,
%T A131319 49,51,53,43,34,54,51,56,56,67,61,55,73,55,67,69,81,65,85,67,82,91,93,
%U A131319 89,97,99,88,89,105,107,89,97,97,89,98,111,121,109,118,105,129,112
%N A131319 Maximal value arising in the sequence S(n) representing the digital sum analog base n of the Fibonacci recurrence.
%C A131319 The respective period lengths of S(n) are given by A001175(n-1) (which is the Pisano period to n-1) for n>=2.
%C A131319 The inequality a(n)<=2n-3 holds for n>2.
%C A131319 a(n)=2n-3 infinitely often; lim sup a(n)/n=2 for n-->oo.
%F A131319 For n=Lucas(2m)=A000032(2m) with m>0, we have a(n)=2n-3.
%F A131319 a(n)=2n-A131320(n).
%e A131319 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.
%e A131319 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.
%Y A131319 Cf. A000032, A000045, A131318, A131320.
%Y A131319 See A010074, A010075, A010076, A010077, A131294, A131295, A131296, A131297 for the definition of the digital sum analog of the Fibonacci recurrence(in different bases).
%K A131319 nonn,base
%O A131319 1,2
%A A131319 _Hieronymus Fischer_, Jul 08 2007