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 A306833 #14 Apr 10 2019 10:23:35
%S A306833 3,5,9,13,25,41,61,121,221,241,265,313,469,529,760
%N A306833 a(1) = 3; a(n+1) is the smallest k > a(n) such that 2^(k-1) == 1 (mod a(n)).
%C A306833 This sequence is finite, the last term a(15) = 760 is even.
%C A306833 Conjecture: for any initial term a(1), this recursion gives a finite sequence (ends with an even term).
%C A306833 Theorem: for odd a(n), a(n+1) is even if and only if ord_{a(n)}(2) is odd and (a(n) mod ord_{a(n)}(2)) is odd.
%C A306833 The set of penultimate terms of the sequences is {A036259} \ {A036260}.
%o A306833 (PARI) lista(nn) = {a = 3; print1(a, ", "); for (n=2, nn, k = a+1; while (Mod(2, a)^(k-1) != 1, k++); a = k; print1(a, ", "); if (!(a%2), break););} \\ _Michel Marcus_, Mar 24 2019
%Y A306833 Cf. A002326, A036259, A036260.
%K A306833 nonn,fini,full
%O A306833 1,1
%A A306833 _Thomas Ordowski_, Mar 12 2019