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%I #7 Apr 28 2024 11:55:53
%S 1,0,3,5,9,11,16,20,23,29,33,39,47,53,62,70,77,87,95,105,117,127,140,
%T 152,163,177,189,203,219,233,250,266,281,299,315,333,353,371,392,412,
%U 431,453,473,495,519,541,566,590,613,639,663,689,717,743,772,800,827,857,885,915,947,977,1010,1042
%N a(n) is the index of the Lucas number that is a ratio of the sum of the first A000217(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 possible Fibonacci number, we always get a Lucas number.
%C A000217() are the triangular numbers.
%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, as 10 is the fourth triangular number, a(4) = 5.
%Y Cf. A000032, A000045, A000071, A000217, A372048, A372049, A372050.
%K nonn
%O 1,3
%A _Tanya Khovanova_ and MIT PRIMES STEP junior group, Apr 17 2024