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%I #9 Apr 28 2024 11:52:00
%S 1,1,0,4,3,3,5,6,5,5,7,8,7,7,9,10,9,9,11,12,11,11,13,14,13,13,15,16,
%T 15,15,17,18,17,17,19,20,19,19,21,22,21,21,23,24,23,23,25,26,25,25,27,
%U 28,27,27,29,30,29,29,31,32,31,31,33,34,33,33,35,36,35,35,37,38,37,37,39,40,39,39,41,42,41
%N a(n) is the index of the Lucas number that is the ratio of the sum of the first n Fibonacci numbers divided by the largest possible Fibonacci number.
%C The sum of the first n Fibonacci numbers is sequence A000071.
%C When we divide the sum by the largest Fibonacci number that divides the sum, we always get a Lucas number.
%C For n > 3, a(n+4) = a(n)+2.
%e The sum of the first ten Fibonacci numbers is 143. The largest Fibonacci that divides this sum is 13, the seventh Fibonacci number. After the division we get 143/13 = 11, the fifth Lucas number. Thus, a(10) = 5.
%Y Cf. A000032, A000045, A000071, A372048.
%K nonn
%O 1,4
%A _Tanya Khovanova_ and MIT PRIMES senior group, Apr 17 2024
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