A217521 Base-4 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

3, 3, 5, 10, 7, 21, 13, 27, 21, 55, 13, 78, 43, 30, 21, 68, 55, 171, 41, 63, 111, 253, 29, 250, 157, 243, 85, 406, 61, 155, 53, 165, 137, 210, 109, 666, 343, 234, 85, 410, 127, 301, 221, 270, 507, 1081, 53, 1029, 501, 204, 313, 1378, 487

Offset: 2

Author

N. J. A. Sloane, Oct 07 2012

Keywords

• nonn

Comments

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

Links

• Charlie Neder, Table of n, a(n) for n = 2..128
• Klaus Sutner and Sam Tetruashvili, Inferring Automatic Sequences.

Crossrefs

Cf. A217519, A217520, A247566-A247581.

Formula

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

Extensions

a(11)-a(20) added (see Inferring Automatic Sequences) by Vincenzo Librandi, Nov 18 2012

a(21)-a(54) from Charlie Neder, Feb 28 2019