This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A372049 #13 Sep 04 2024 15:52:25 %S A372049 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 A372049 15,15,17,18,17,17,19,20,19,19,21,22,21,21,23,24,23,23,25,26,25,25,27, %U A372049 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 A372049 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 A372049 The sum of the first n Fibonacci numbers is sequence A000071. %C A372049 When we divide the sum by the largest Fibonacci number that divides the sum, we always get a Lucas number. %C A372049 For n > 3, a(n+4) = a(n)+2. %H A372049 Tanya Khovanova and the MIT PRIMES STEP senior group, <a href="https://arxiv.org/abs/2409.01296">Fibonacci Partial Sums Tricks</a>, arXiv:2409.01296 [math.HO], 2024. %e A372049 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 A372049 Cf. A000032, A000045, A000071, A372048. %K A372049 nonn %O A372049 1,4 %A A372049 _Tanya Khovanova_ and MIT PRIMES senior group, Apr 17 2024