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 A372051 #7 Apr 28 2024 11:55:53 %S A372051 1,0,3,5,9,11,16,20,23,29,33,39,47,53,62,70,77,87,95,105,117,127,140, %T A372051 152,163,177,189,203,219,233,250,266,281,299,315,333,353,371,392,412, %U A372051 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 A372051 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 A372051 The sum of the first n Fibonacci numbers is sequence A000071. %C A372051 When we divide the sum by the largest possible Fibonacci number, we always get a Lucas number. %C A372051 A000217() are the triangular numbers. %e A372051 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 A372051 Cf. A000032, A000045, A000071, A000217, A372048, A372049, A372050. %K A372051 nonn %O A372051 1,3 %A A372051 _Tanya Khovanova_ and MIT PRIMES STEP junior group, Apr 17 2024