A217521 - OEIS

%I #18 Mar 02 2019 11:58:53

%S 3,3,5,10,7,21,13,27,21,55,13,78,43,30,21,68,55,171,41,63,111,253,29,

%T 250,157,243,85,406,61,155,53,165,137,210,109,666,343,234,85,410,127,

%U 301,221,270,507,1081,53,1029,501,204,313,1378,487

%N Base-4 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

%C Also the number of distinct words which can be formed from (123..n)* by taking every 4^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 Charlie Neder, <a href="/A217521/b217521.txt">Table of n, a(n) for n = 2..128</a>

%H Klaus Sutner and Sam Tetruashvili, <a href="http://www.cs.cmu.edu/~sutner/papers/auto-seq.pdf">Inferring Automatic Sequences</a>.

%F a(n) <= A217519(n). In particular, it appears that a(n) = A217519(n)/2 whenever this result is an integer, and a(n) = A217519(n) for n = 2, 7, 14, 23, 31, 46, 47, 49, 62, 71, 89, 94, 98... - _Charlie Neder_, Feb 28 2019

%Y Cf. A217519, A217520, A247566-A247581.

%K nonn

%O 2,1

%A _N. J. A. Sloane_, Oct 07 2012

%E a(11)-a(20) added (see Inferring Automatic Sequences) by _Vincenzo Librandi_, Nov 18 2012

%E a(21)-a(54) from _Charlie Neder_, Feb 28 2019