cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A247566 Base-5 state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...n)*.

Original entry on oeis.org

2, 6, 4, 6, 12, 42, 16, 54, 11, 55, 24, 52, 84, 31, 64, 272, 108, 171, 21
Offset: 2

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Author

Vincenzo Librandi, Sep 20 2014

Keywords

Links

Crossrefs

Cf. base-k state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (12...n)*: A217519 (k=2), A217520 (k=3), A217521 (k=4), this sequence (k=5), A247567 (k=6), A247568 (k=7), A247569 (k=8), A247570 (k=9), A247571 (k=10), A247572 (k=11), A247573 (k=12), A247574 (k=13), A247575 (k=14), A247576 (k=15), A247577 (k=16), A247578 (k=17), A247579 (k=18), A247580 (k=19), A247581 (k=20).

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

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Oct 07 2012

Keywords

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

Crossrefs

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

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

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

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

Views

Author

N. J. A. Sloane, Oct 07 2012

Keywords

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

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

A306640 Array read by antidiagonals: A(n,k) (n,k >= 2) is the base-n state complexity of the partitioned finite deterministic automaton (PFDA) for the periodic sequence (123..k)*.

Original entry on oeis.org

3, 6, 2, 7, 4, 3, 20, 8, 3, 2, 13, 20, 5, 6, 3, 21, 7, 10, 4, 4, 2, 15, 42, 7, 6, 9, 3, 3, 54, 16, 21, 12, 5, 8, 6, 2, 41, 13, 13, 42, 7, 20, 5, 4, 3, 110, 40, 27, 16, 14, 6, 20, 4, 3, 2, 27, 55, 21, 54, 23, 8, 13, 10, 9, 6, 3, 156, 25, 55, 11
Offset: 1

Views

Author

Charlie Neder, Mar 02 2019

Keywords

Comments

Rows are ultimately periodic.

Examples

			Array begins:
   3   2   3   2   3
   6   4   3   6   4
   7   8   5   4   9  ...
  20  20  10   6   5
  13   7   7  12   7
          ...

Links

Crossrefs

Columns: A217519-A217521 (n = 2-4), A247566-A247581 (n = 5-20).
Rows: A217515-A217518 (k = 3-6), A247387-A247391 (k = 7-11), A247434-A247442 (k = 12-20).

Formula

A(n,n^k) = Sum_{i=0..k} n^i.
A(n+1,n) = n.
It also appears that A(n-1,n) = 2n.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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