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%I #18 May 01 2024 01:46:59
%S 2,3,2,2,4,5,4,4,6,7,6,6,8,9,8,8,10,11,10,10,12,13,12,12,14,15,14,14,
%T 16,17,16,16,18,19,18,18,20,21,20,20,22,23,22,22,24,25,24,24,26,27,26,
%U 26,28,29,28,28,30,31,30,30,32,33,32,32,34,35,34,34,36,37,36,36,38,39,38,38,40,41,40,40
%N The index of the largest Fibonacci number that divides the sum of Fibonacci numbers with indices 1 through n.
%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)+1.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1).
%e The sum of the first ten Fibonacci numbers is 143. The largest Fibonacci that divides this sum is 13, the seventh Fibonacci number. Thus, a(10) = 7. After the division we get 143/13 = 11, the fifth Lucas number.
%t LinearRecurrence[{2,-2,2,-1},{2,3,2,2},80] (* _James C. McMahon_, Apr 30 2024 *)
%Y Cf. A000032, A000045, A000071, A054494, A075850, A372049.
%K nonn,easy
%O 1,1
%A _Tanya Khovanova_ and the MIT PRIMES STEP senior group, Apr 17 2024
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