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 A381053 #77 Jun 12 2025 00:50:28 %S A381053 1,2,34,46,68,92,94,106,166,188,212,214,226,274,332,334,346,394,428, %T A381053 452,454,466,514,526,548,586,634,646,668,692,694,706,754,766,788,886, %U A381053 908,932,934,1006,1028,1052,1114,1126,1172,1174,1186,1234,1268,1292,1294,1306 %N A381053 Integers k such that Fibonacci(k) is odd and divides the sum of the first Fibonacci(k) nonzero Fibonacci numbers. %C A381053 Has infinitely many members. %C A381053 Subsequence of A383021. %C A381053 Contains all 2p and 4p such that p is an odd prime and p == 2,8 (mod 15). %H A381053 Amirali Fatehizadeh and Daniel Yaqubi, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL25/Yaqubi/yaq6.html">Average of the Fibonacci numbers</a>, J. Integer Seq. 25 (2022), no. 2, Art. 22.2.6, 10 pp. %H A381053 Oisín Flynn-Connolly, <a href="https://arxiv.org/abs/2504.09938">On the divisibility of sums of Fibonacci numbers</a>, arXiv:2504.09938 [math.NT], 2025. %H A381053 Michal Křížek and Lawrence Somer, <a href="https://math.colgate.edu/~integers/y36/y36.pdf">Period lengths modulo n and average of terms of second order linear recurrences</a>, Integers 24 (2024), Paper No. A36, 41 pp. %e A381053 For k =2, Fibonacci(2) = 1, which is odd, and Fibonacci(Fibonacci(1)) = Fibonacci(1) = 1, which is divisible by 1. %e A381053 For k = 34, Fibonacci(34) = 5702887 is odd, and Fibonacci(1) + Fibonacci(2) + ... + Fibonacci(5702887) = Fibonacci(5702889) - 1, which is divisible by Fibonacci(34) = 5702887. %Y A381053 Cf. A000045, A158569, A331976, A383021, A331977. %K A381053 nonn %O A381053 1,2 %A A381053 _Oisín Flynn-Connolly_, Apr 14 2025 %E A381053 More terms from _Alois P. Heinz_, Apr 14 2025