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%I #8 Jul 10 2015 19:58:16
%S 1,2,3,3,5,3,3,3,5,3,3,11,7,3,3,6,9,3,3,8,9,10,11,3,9,3,3,3,15,26,8,
%T 13,10,12,3,11,19,3,23,13,13,3,21,3,23,10,3,3,9,3,3,16,17,3,3,23,17,
%U 19,29,22,11,3,17,10,25,3,22,3,35,30,11,29,57,3,3,17,65,16,13,20,21,3,3
%N 2*n - maximal value arising in the sequence S(n) representing the digital sum analog base n of the Fibonacci recurrence.
%C The inequality a(n)>=3 holds for n>2.
%C a(n)=3 arises infinitely often; lim inf a(n)=3 for n-->oo.
%F a(n)=2n-A131319(n).
%F a(Lucas(2n))=3 where Lucas(n)=A000032(n).
%e a(3)=3, since the digital sum analog base 3 of the Fibonacci sequence is 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 which implies 2*3-3=3. a(9)=5, because the pattern here is {2,3,5,8,13,13,10,7,9,8,9,9} (see A010076) where the maximal value is 13 and so 2*9-13=5.
%Y Cf. A000032, A000045, A000032, A131318, A131320.
%Y See A010074, A010075, A010076, A010077, A131294, A131295, A131296, A131297 for the definition of the digital sum analog of the Fibonacci sequence (in different bases).
%K nonn,base
%O 1,2
%A _Hieronymus Fischer_, Jul 08 2007
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