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A217519
Base-2 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.
5
3, 6, 7, 20, 13, 21, 15, 54, 41, 110, 27, 156, 43, 60, 31, 136, 109, 342, 83, 126, 221, 253, 55, 500, 313, 486, 87, 812, 121, 155, 63, 330, 273, 420, 219, 1332, 685, 468, 167, 820, 253, 602, 443, 540, 507, 1081, 111, 1029, 1001, 408, 627, 2756, 973
OFFSET
2,1
COMMENTS
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
LINKS
Savinien Kreczman, Luca Prigioniero, Eric Rowland, and Manon Stipulanti, Magic numbers in periodic sequences, Univ. Liège (Belgium, 2023).
Klaus Sutner and Sam Tetruashvili, Inferring Automatic Sequences.
FORMULA
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
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 07 2012
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
STATUS
approved