A217520 Base-3 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

2, 4, 8, 20, 7, 42, 16, 13, 40, 55, 25, 39, 84, 61, 64, 272, 22, 342, 80, 127, 110, 253, 49, 500, 78, 40, 168, 812, 121, 930, 256, 166, 544, 420, 76, 666, 684, 118, 160, 328, 253, 1806, 440, 184, 506, 1081, 193, 2058, 1000, 817, 312, 2756, 67

Offset: 2

Author

N. J. A. Sloane, Oct 07 2012

Keywords

• nonn

Comments

Also the number of distinct words that can be formed from (123..n)* by taking every 3^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..100
• Klaus Sutner and Sam Tetruashvili, Inferring Automatic Sequences.

Crossrefs

Cf. A217519, A217521, A247566-A247581, A019334.

Formula

a(3^k) = (3^(k+1)-1)/2. It appears that a(n) <= n(n-1), with equality if and only if n is a prime with primitive root 3 (A019334). - 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