A247566 -id:A247566 - cp's OEIS frontend

A217519 Base-2 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

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

N. J. A. Sloane, Oct 07 2012

nonn

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

Charlie Neder, Table of n, a(n) for n = 2..128
Savinien Kreczman, Luca Prigioniero, Eric Rowland, and Manon Stipulanti, Magic numbers in periodic sequences, arXiv:2304.03268 [cs.FL] (2023).
Klaus Sutner and Sam Tetruashvili, Inferring Automatic Sequences.

Cf. A217520, A217521, A247566-A247581, A001122.

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

Neder's conjecture was proved by Kreczman, Prigioniero, Rowland, and Stipulanti. - Eric Rowland, Feb 02 2025

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

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

Original entry on oeis.org

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

N. J. A. Sloane, Oct 07 2012

nonn

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

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

Cf. A217519, A217520, A247566-A247581.

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

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

A247581 Base-20 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

Original entry on oeis.org

3, 6, 5, 6, 13, 14, 17, 54, 11, 55, 25, 156, 29, 31, 33, 272, 109, 19, 21

Offset: 2

Vincenzo Librandi, Sep 20 2014

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).

Cf. similar sequences listed in A247566.

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

Original entry on oeis.org

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

N. J. A. Sloane, Oct 07 2012

nonn

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

Charlie Neder, Table of n, a(n) for n = 2..100
Klaus Sutner and Sam Tetruashvili, Inferring Automatic Sequences.

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

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

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

A247567 Base-6 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

Original entry on oeis.org

3, 4, 9, 5, 7, 14, 23, 16, 11, 110, 19, 156, 29, 16, 55, 272, 25, 171, 27

Offset: 2

Vincenzo Librandi, Sep 20 2014

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).

Cf. similar sequences listed in A247566.

A247568 Base-7 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

Original entry on oeis.org

2, 3, 8, 20, 6, 8, 16, 27, 40, 110, 24, 156, 15, 60, 32, 272, 54, 57, 80

Offset: 2

Vincenzo Librandi, Sep 20 2014

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).

Cf. similar sequences listed in A247566.

A247569 Base-8 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

Original entry on oeis.org

3, 6, 5, 20, 13, 7, 9, 18, 41, 110, 25, 52, 15, 60, 25, 136, 37, 114, 81

Offset: 2

Vincenzo Librandi, Sep 20 2014

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).

Cf. similar sequences listed in A247566.

A247570 Base-9 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

Original entry on oeis.org

2, 4, 4, 10, 7, 21, 8, 10, 20, 55, 13, 39, 42, 31, 32, 136, 19, 171, 40

Offset: 2

Vincenzo Librandi, Sep 20 2014

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).

Cf. similar sequences listed in A247566.

A247571 Base-10 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

Original entry on oeis.org

3, 3, 9, 6, 7, 42, 25, 9, 11, 22, 23, 78, 85, 16, 59, 272, 19, 342, 31

Offset: 2

Vincenzo Librandi, Sep 20 2014

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).

Cf. similar sequences listed in A247566.

A247572 Base-11 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

Original entry on oeis.org

2, 6, 8, 5, 12, 21, 16, 54, 10, 12, 24, 156, 42, 30, 64, 272, 108, 57, 40

Offset: 2

Vincenzo Librandi, Sep 20 2014

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).

Cf. similar sequences listed in A247566.

cp's OEIS Frontend

A217519 Base-2 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

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

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A247581 Base-20 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

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

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A247567 Base-6 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

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A247568 Base-7 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

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A247569 Base-8 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

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Author

Keywords

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A247570 Base-9 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

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Author

Keywords

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A247571 Base-10 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

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Author

Keywords

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A247572 Base-11 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

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Author

Keywords

Links

Crossrefs