A001968 -id:A001968 - cp's OEIS frontend

A125592 Evil numbers (A001969) multiplied by 2.

0, 6, 10, 12, 18, 20, 24, 30, 34, 36, 40, 46, 48, 54, 58, 60, 66, 68, 72, 78, 80, 86, 90, 92, 96, 102, 106, 108, 114, 116, 120, 126, 130, 132, 136, 142, 144, 150, 154, 156, 160, 166, 170, 172, 178, 180, 184, 190, 192, 198, 202, 204, 210, 212, 216, 222, 226, 228, 232, 238

Offset: 1

Luis H. Gallardo and Johan Huisman, Jan 07 2007

Numbers n such that the Maple command genpoly(n,2,t) outputs a polynomial in F_2[t] that is divisible by t(t+1), where F_2 is the finite field with two elements. E.g. a(2)=10 since the polynomial genpoly(10,2,t)=t^3+t = t(t+1)(t+1) in F_2[t] is divisible by the polynomial t(t+1) in F_2[t]

These are the even evil numbers: the intersection of A001968 and A005843. - Tanya Khovanova, May 04 2007

2*Select[Range[0,120],EvenQ[DigitCount[#,2,1]]&] (* Harvey P. Dale, Jun 14 2017 *)

is(n)=n%2==0 && hammingweight(n)%2==0 \\ Charles R Greathouse IV, Mar 22 2013

a(n)=4*n--+hammingweight(n)%2*2 \\ Charles R Greathouse IV, Mar 22 2013

A001963 Winning positions in the u-pile of the 4-Wythoff game with i=1.

Original entry on oeis.org

0, 1, 2, 4, 5, 6, 7, 8, 10, 11, 12, 13, 15, 16, 17, 18, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 65, 67, 68, 69, 70, 72, 73, 74, 75, 76, 78, 79, 80, 81, 83

Offset: 0

N. J. A. Sloane

See Connell (1959) for further information.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..10000
Ian G. Connell, A generalization of Wythoff's game, Canad. Math. Bull. 2 (1959) 181-190

Cf. A001954, A001958, A001959, A001964-A001968.

Table[Floor[(n + 1/4)*(Sqrt[5] - 1)], {n, 0, 100}] (* T. D. Noe, Aug 17 2012 *)

a(n) = floor( (n+1/4)*(sqrt(5)-1) ). - R. J. Mathar, Feb 14 2011

Edited by Hugo Pfoertner, Dec 27 2021

A001960 a(n) = floor((n+2/3)*(5+sqrt(13))/2); v-pile positions in the 3-Wythoff game.

Original entry on oeis.org

2, 7, 11, 15, 20, 24, 28, 32, 37, 41, 45, 50, 54, 58, 63, 67, 71, 76, 80, 84, 88, 93, 97, 101, 106, 110, 114, 119, 123, 127, 131, 136, 140, 144, 149, 153, 157, 162, 166, 170, 174, 179, 183, 187, 192, 196, 200, 205, 209, 213, 218, 222, 226, 230, 235, 239, 243, 248

Offset: 0

N. J. A. Sloane

nonn

3-Wythoff game, i=2, the v-pile positions in the Connell terminology. - R. J. Mathar, Feb 14 2011

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..10000
Ian G. Connell, A generalization of Wythoff's game, Canad. Math. Bull. 2 (1959) 181-190.

Complement of A001957.

Cf. A001954, A001958, A001959, A001963-A001968.

Table[Floor[(n + 2/3)*(5 + Sqrt[13])/2], {n, 0, 100}] (* T. D. Noe, Aug 17 2012 *)

a(n) = floor((n+2/3)*(5+sqrt(13))/2). - R. J. Mathar, Feb 14 2011

New name from Hugo Pfoertner, Dec 27 2021

A001959 u-pile numbers for the 3-Wythoff game with i=2.

Original entry on oeis.org

0, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 26, 28, 29, 30, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 45, 46, 47, 49, 50, 51, 52, 54, 55, 56, 58, 59, 60, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 80, 81, 82, 84, 85, 86, 88

Offset: 0

N. J. A. Sloane

See Connell (1959) for further information.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..10000
Ian G. Connell, A generalization of Wythoff's game, Canad. Math. Bull. 2 (1959) 181-190

Cf. A001954, A001958, A001960, A001963-A001968.

Table[Floor[(n + 2/3)*(Sqrt[13] - 1)/2], {n, 0, 100}] (* T. D. Noe, Aug 17 2012 *)

a(n) = floor( (n+2/3)*(sqrt(13)-1)/2 ). - R. J. Mathar, Feb 14 2011

Edited by Hugo Pfoertner, Dec 27 2021

A001957 u-pile positions in the 3-Wythoff game with i=1.

Original entry on oeis.org

0, 1, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 25, 26, 27, 29, 30, 31, 33, 34, 35, 36, 38, 39, 40, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 68, 69, 70, 72, 73, 74, 75, 77, 78, 79, 81, 82, 83, 85, 86, 87

Offset: 0

N. J. A. Sloane

See Connell (1959) for further information.

The complement is A001960. - Omar E. Pol, Jan 06 2009

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..10000
Ian G. Connell, A generalization of Wythoff's game, Canad. Math. Bull. 2 (1959) 181-190.

Cf. A001954, A001958-A001960, A001963-A001968.

Table[Floor[(n + 1/3)*(Sqrt[13] - 1)/2], {n, 0, 100}] (* T. D. Noe, Aug 17 2012 *)

a(n) = floor((n+1/3)*(sqrt(13)-1)/2). - R. J. Mathar, Feb 14 2011

Edited by N. J. A. Sloane, Dec 27 2021

A001967 u-pile positions for the 4-Wythoff game with i=3.

Original entry on oeis.org

0, 2, 3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 49, 50, 51, 52, 54, 55, 56, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 70, 71, 72, 73, 75, 76, 77, 78, 80, 81, 82, 83

Offset: 0

N. J. A. Sloane

See Connell (1959) for further information.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..10000
Ian G. Connell, A generalization of Wythoff's game, Canad. Math. Bull. 2 (1959) 181-190.

Cf. A001968 (v-pile).

Table[Floor[(n + 3/4)*(Sqrt[5] - 1)], {n, 0, 100}] (* T. D. Noe, Aug 17 2012 *)

a(n) = floor( (n+3/4)*(sqrt(5)-1) ). - R. J. Mathar, Feb 14 2011

Edited by Hugo Pfoertner, Dec 27 2021

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A125592 Evil numbers (A001969) multiplied by 2.

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A001963 Winning positions in the u-pile of the 4-Wythoff game with i=1.

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A001960 a(n) = floor((n+2/3)*(5+sqrt(13))/2); v-pile positions in the 3-Wythoff game.

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A001959 u-pile numbers for the 3-Wythoff game with i=2.

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A001957 u-pile positions in the 3-Wythoff game with i=1.

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A001967 u-pile positions for the 4-Wythoff game with i=3.

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