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 A331977 #24 Aug 22 2025 19:32:17 %S A331977 1,6479,11663,34943,47519,51983,196559,327359,685583,954239,1016063, %T A331977 1346879,2039183,2332799,2504447,4665599,5143823,5962319,6128639, %U A331977 6723359,7225343,9363599,12027023,12446783,14930351,17639999,17735759,22924943,24681023,34715519,41990399 %N A331977 Integers m such that m and m+1 are terms of A111035. %C A331977 Sequence is infinite as proved by Luca and Marques (2025). - _Max Alekseyev_, Aug 22 2025 %H A331977 Daniel Suteu, <a href="/A331977/b331977.txt">Table of n, a(n) for n = 1..128</a> %H A331977 Florian Luca and Diego Marques, <a href="https://doi.org/10.1007/s00013-025-02166-2">On integral consecutive arithmetic means of the first Fibonacci numbers</a>. Arch. Math. (2025). %H A331977 Daniel Yaqubi and Amirali Fatehizadeh, <a href="https://arxiv.org/abs/2001.11839">Some results on average of Fibonacci and Lucas sequences</a>, arXiv:2001.11839 [math.CO], 2020. %o A331977 (PARI) f(n,m) = (Mod([1,1;1,0], m)^n)[1,2]; %o A331977 isok(n) = f(n+2,n)==1 && f(n+3, n+1)==1; %o A331977 for(k=1, 10^7, if(isok(k), print1(k, ", "))); \\ _Daniel Suteu_, Feb 03 2020 %Y A331977 Cf. A111035 (the sum of the first k nonzero Fibonacci numbers is divisible by k). %K A331977 nonn %O A331977 1,2 %A A331977 _Michel Marcus_, Feb 03 2020 %E A331977 a(23)-a(31) from _Daniel Suteu_, Feb 03 2020