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 A217519 #37 Feb 03 2025 22:55:47 %S A217519 3,6,7,20,13,21,15,54,41,110,27,156,43,60,31,136,109,342,83,126,221, %T A217519 253,55,500,313,486,87,812,121,155,63,330,273,420,219,1332,685,468, %U A217519 167,820,253,602,443,540,507,1081,111,1029,1001,408,627,2756,973 %N A217519 Base-2 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*. %C A217519 Also the number of infinite words that can be formed from (123..n)* by taking every 2^k-th term from some initial index i, with i and k nonnegative. (Follows from Case 2 of Theorem 2.1) - _Charlie Neder_, Feb 28 2019 %H A217519 Charlie Neder, <a href="/A217519/b217519.txt">Table of n, a(n) for n = 2..128</a> %H A217519 Savinien Kreczman, Luca Prigioniero, Eric Rowland, and Manon Stipulanti, <a href="https://arxiv.org/abs/2304.03268">Magic numbers in periodic sequences</a>, arXiv:2304.03268 [cs.FL] (2023). %H A217519 Klaus Sutner and Sam Tetruashvili, <a href="http://www.cs.cmu.edu/~sutner/papers/auto-seq.pdf">Inferring Automatic Sequences</a>. %F A217519 a(2^k) = 2^(k+1) - 1. It appears that a(n) <= n(n-1), with equality if and only if n is a prime with primitive root 2 (A001122). - _Charlie Neder_, Feb 28 2019 %F A217519 Neder's conjecture was proved by Kreczman, Prigioniero, Rowland, and Stipulanti. - _Eric Rowland_, Feb 02 2025 %Y A217519 Cf. A217520, A217521, A247566-A247581, A001122. %K A217519 nonn %O A217519 2,1 %A A217519 _N. J. A. Sloane_, Oct 07 2012 %E A217519 a(11)-a(20) added (see Inferring Automatic Sequences) by _Vincenzo Librandi_, Nov 18 2012 %E A217519 a(21)-a(54) from _Charlie Neder_, Feb 28 2019