A176059 -id:A176059 - cp's OEIS frontend

A247389 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123456789)*.

Original entry on oeis.org

54, 13, 27, 54, 16, 27, 18, 10, 9, 54, 19, 27, 54, 19, 27, 18, 10, 9, 54

Offset: 2

Vincenzo Librandi, Sep 16 2014

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

Cf. A176059, A217515 - A217518, A247387.

A247434 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123.....12)*.

Original entry on oeis.org

27, 25, 13, 24, 19, 24, 25, 13, 23, 24, 13, 12, 37, 25, 13, 24, 25, 24, 25

Offset: 2

Vincenzo Librandi, Sep 19 2014

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

Cf. A176059, A217515 - A217518, A247387, A247390, A247391.

A247442 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...20)*.

Original entry on oeis.org

83, 80, 41, 21, 27, 80, 81, 40, 31, 40, 81, 80, 55, 41, 21, 80, 99, 40, 21

Offset: 2

Vincenzo Librandi, Sep 20 2014

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

Cf. A176059, A217515 - A217518, A247387, A247390, A247391.

A281006 a(n) = A000203(n) - A052928(n-1).

Original entry on oeis.org

1, 3, 2, 5, 2, 8, 2, 9, 5, 10, 2, 18, 2, 12, 10, 17, 2, 23, 2, 24, 12, 16, 2, 38, 7, 18, 14, 30, 2, 44, 2, 33, 16, 22, 14, 57, 2, 24, 18, 52, 2, 56, 2, 42, 34, 28, 2, 78, 9, 45, 22, 48, 2, 68, 18, 66, 24, 34, 2, 110, 2, 36, 42, 65, 20, 80, 2, 60, 28, 76, 2, 125, 2, 42, 50, 66, 20, 92, 2, 108, 41, 46, 2, 142, 24, 48, 34, 94, 2

Offset: 1

Omar E. Pol, Jan 23 2017

nonn

a(n) = 2 iff n is an odd prime (A065091).

Has a symmetric representation as a narrow pyramid with holes, in the same way as A249351.

			A000203    A052928     a(n)
.   1    -    0    =    1
.   3    -    0    =    3
.   4    -    2    =    2
.   7    -    2    =    5
.   6    -    4    =    2
.  12    -    4    =    8
...

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to sigma(n)

Cf. A000203, A004526, A048050, A052928, A065091, A176059, A196020, A235791, A236104, A237048, A237270, A237271, A237591, A237593, A245092, A249351, A262626, A279387, A281010.

A281006(n) = (sigma(n) - 2*((n-1)>>1)); \\ Antti Karttunen, Sep 25 2018

a(n) = sigma(n) - 2*floor((n - 1)/2) = A000203(n) - 2*A004526(n-1).

a(n) = A048050(n) + A176059(n), n >= 2.

A247388 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (12345678)*.

Original entry on oeis.org

15, 16, 13, 16, 23, 16, 9, 8, 25, 16, 17, 16, 25, 16, 9, 8, 25, 16, 17

Offset: 2

Vincenzo Librandi, Sep 16 2014

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

Cf. A176059, A217515 - A217518, A247387.

A247435 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123....13)*.

Original entry on oeis.org

156, 39, 78, 52, 156, 156, 52, 39, 78, 156, 26, 14, 13, 156, 39, 78, 52, 156, 156, 52, 39, 78, 156, 26, 14, 13, 156, 39, 78, 52, 156, 156, 52, 39, 78, 156, 26, 14, 13, 156, 39, 78, 52, 156, 156, 52, 39, 78, 156, 26, 14, 13, 156, 39, 78, 52, 156, 156, 52, 39

Offset: 2

Vincenzo Librandi, Sep 19 2014

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A176059, A217515 - A217518, A247387, A247389 - A247391.

&cat[[156, 39, 78, 52, 156, 156, 52, 39, 78, 156, 26, 14, 13]: n in [0..10]];

CoefficientList[Series[(156 + 39 x + 78 x^2 + 52 x^3 + 156 x^4 + 156 x^5 + 52 x^6 + 39 x^7 + 78 x^8 + 156 x^9 + 26 x^10 + 14 x^11 + 13 x^12)/(1 - x^13), {x, 0, 60}], x]
PadRight[{},120,{156,39,78,52,156,156,52,39,78,156,26,14,13}] (* Harvey P. Dale, Mar 19 2021 *)

G.f.: x^2*(156 + 39*x + 78*x^2 + 52*x^3 + 156*x^4 + 156*x^5 + 52*x^6 + 39*x^7 + 78*x^8 + 156*x^9 + 26*x^10 + 14*x^11 + 13*x^12)/(1 - x^13).

A247436 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...14)*.

Original entry on oeis.org

43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14, 43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14, 43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14, 43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14, 43, 84, 43, 84, 29, 15, 15, 42

Offset: 2

Vincenzo Librandi, Sep 19 2014

Period 14, repeat [43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14].

Klaus Sutner and Sam Tetruashvili, Inferring automatic sequences (see table on the p. 5).
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A176059, A217515 - A217518, A247387 - A247391.

&cat[[43, 84, 43, 84, 29, 15, 15, 42, 85, 42, 85, 28, 15, 14]: n in [0..10]];

CoefficientList[Series[(43 + 84 x + 43 x^2 + 84 x^3 + 29 x^4 + 15 x^5 + 15 x^6 + 42 x^7 + 85 x^8 + 42 x^9 + 85 x^10 + 28 x^11 + 15 x^12 + 14 x^13)/(1 - x^14), {x, 0, 60}], x]

G.f.: -x^2*(43+84*x+43*x^2+84*x^3+29*x^4+15*x^5+15*x^6+42*x^7+85*x^8+42*x^9+85
*x^10+28*x^11+15*x^12+14*x^13) / ( (x-1)*(1+x^6+x^5+x^4+x^3+x^2+x)*(1+x)*(1-x+
x^2-x^3+x^4-x^5+x^6) ).

A247437 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...15)*.

Original entry on oeis.org

60, 61, 30, 31, 16, 60, 60, 31, 16, 30, 61, 60, 30, 16, 15, 60, 61, 30, 31

Offset: 2

Vincenzo Librandi, Sep 20 2014

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

Cf. A176059, A217515 - A217518, A247387, A247390, A247391.

A247438 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...16)*.

Original entry on oeis.org

31, 64, 21, 64, 55, 32, 25, 32, 59, 64, 29, 64, 63, 32, 17, 16, 65, 64, 33

Offset: 2

Vincenzo Librandi, Sep 20 2014

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

Cf. A176059, A217515 - A217518, A247387, A247390, A247391.

A247439 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...17)*.

Original entry on oeis.org

136, 272, 68, 272, 272, 272, 136, 136, 272, 272, 272, 68, 272, 136, 34, 18, 17, 136, 272

Offset: 2

Vincenzo Librandi, Sep 20 2014

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

Cf. A176059, A217515 - A217518, A247387, A247390, A247391.

cp's OEIS Frontend

A247389 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123456789)*.

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A247434 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123.....12)*.

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A247442 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...20)*.

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A281006 a(n) = A000203(n) - A052928(n-1).

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A247388 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (12345678)*.

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A247435 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123....13)*.

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A247436 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...14)*.

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A247437 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...15)*.

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A247438 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...16)*.

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A247439 Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123...17)*.

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