Tanbir Ahmed - cp's OEIS frontend

A217236 Van der Waerden numbers w(j+2; t_0,t_1,...,t_{j-1}, 4, 5) with t_0 = t_1 = ... = t_{j-1} = 2.

55, 71, 75, 79

Offset: 0

Tanbir Ahmed, Sep 28 2012

			w(2;4,5)=55, w(3; 2, 4, 5)=71, and so on...

T. C. Brown, Some new van der Waerden numbers (preliminary report), Notices American Math. Society, 21 (1974), A-432.
V. Chvatal, Some unknown van der Waerden numbers, Combinatorial Structures and their Applications (R. Guy et al., eds.), Gordon and Breach, New York, 1970.

T. Ahmed, Some new van der Waerden numbers and some van der Waerden-type numbers, Integers, 9 (2009), A06, 65-76.

Cf. A217005, A217007, A217008, A217058, A217059, A217060, A217237.

A217237 Van der Waerden numbers w(j+2; t_0,t_1,...,t_{j-1}, 4, 6) with t_0 = t_1 = ... = t_{j-1} = 2.

Original entry on oeis.org

73, 83, 93, 101

Offset: 0

Tanbir Ahmed, Sep 28 2012

			w(2;4,6)=73, w(3;2,4,6)=83, and so on...

T. Ahmed, Some new van der Waerden numbers and some van der Waerden-type numbers, Integers, 9 (2009), A06, 65-76.
M. D. Beeler and P. E. O'Neil, Some new Van der Waerden numbers, Discrete Math., 28 (1979), 135-146.
Michal Kouril, Computing the van der Waerden number W(3,4)=293, INTEGERS 12 (2012), A46.
B. Landman, A. Robertson, and C. Culver, Some new exact van der Waerden numbers, Integers, 5(2) (2005), A10.

Cf. A217005, A217007, A217008, A217058, A217059, A217060, A217236.

A217235 Van der Waerden numbers w(3; 3, 3, n).

Original entry on oeis.org

27, 51, 80, 107

Offset: 3

Tanbir Ahmed, Sep 28 2012

			w(3; 3, 3, 3)=27, w(3; 3, 3, 4) = 51, and so on...

V. Chvatal, Some unknown van der Waerden numbers, Combinatorial Structures and their Applications (R. Guy et al., eds.), Gordon and Breach, New York, 1970.

Tanbir Ahmed, On computation of exact van der Waerden numbers, Integers: Electronic Journal of Combinatorial Number Theory, 11 (2011), A71.
M. D. Beeler and P. E. O'Neil, Some new Van der Waerden numbers, Discrete Math., 28 (1979), 135-146.
B. Landman, A. Robertson, and C. Culver, Some new exact van der Waerden numbers, Integers, 5(2) (2005), A10.

Cf. A171081, A171082, A217037.

A217060 Van der Waerden numbers w(j+2; t_0,t_1,...,t_{j-1}, 3, 6) with t_0 = t_1 = ... = t_{j-1} = 2.

Original entry on oeis.org

32, 40, 48, 56, 60, 65, 71

Offset: 0

Tanbir Ahmed, Sep 25 2012

T. C. Brown, Some new van der Waerden numbers (preliminary report), Notices American Math. Society, 21 (1974), A-432.
V. Chvatal, Some unknown van der Waerden numbers, Combinatorial Structures and their Applications (R. Guy et al., eds.), Gordon and Breach, New York, 1970.

T. Ahmed, Some new van der Waerden numbers and some van der Waerden-type numbers, Integers, 9 (2009), A06, 65-76.
T. Ahmed, Some more Van der Waerden numbers, J. Int. Seq. 16 (2013) 13.4.4
B. Landman, A. Robertson, and C. Culver, Some new exact van der Waerden numbers, Integers, 5(2) (2005), A10.

Cf. A217005, A217007, A217008, A217058, A217059, A217236, A217237.

a(6)=71 added by Tanbir Ahmed, Dec 07 2012

A217059 Van der Waerden numbers w(j+2; t_0,t_1,...,t_{j-1}, 3, 5) with t_0 = t_1 = ... = t_{j-1} = 2.

Original entry on oeis.org

22, 32, 43, 44, 50, 55, 61, 65, 70

Offset: 0

Tanbir Ahmed, Sep 25 2012

			w(2;3,5)=22, w(3;2,3,5)=32, w(4;2,2,3,5)=43, and so on...

T. C. Brown, Some new van der Waerden numbers (preliminary report), Notices American Math. Society, 21 (1974), A-432.
V. Chvatal, Some unknown van der Waerden numbers, Combinatorial Structures and their Applications (R. Guy et al., eds.), Gordon and Breach, New York, 1970.

T. Ahmed, Some new van der Waerden numbers and some van der Waerden-type numbers, Integers, 9 (2009), A06, 65-76.
T. Ahmed, On computation of exact van der Waerden numbers, Integers: Electronic Journal of Combinatorial Number Theory, 11 (2011), A71.
T. Ahmed, Some more Van der Waerden numbers, J. Int. Seq. 16 (2013) 13.4.4

Cf. A217005, A217007, A217008, A217058, A217060, A217236, A217237.

a(8) = 70 from Tanbir Ahmed, Mar 11 2013

A217058 Van der Waerden numbers w(j+2; t_0,t_1,...,t_{j-1}, 3, 4) with t_0 = t_1 = ... = t_{j-1} = 2.

Original entry on oeis.org

18, 21, 25, 29, 33, 36, 40, 42, 45, 48, 52, 55

Offset: 0

Tanbir Ahmed, Sep 25 2012

			w(2;3,4)=18, w(3;2,3,4)=21, w(4;2,2,3,4)=25, and so on...

T. C. Brown, Some new van der Waerden numbers (preliminary report), Notices American Math. Society, 21 (1974), A-432.
V. Chvatal, Some unknown van der Waerden numbers, Combinatorial Structures and their Applications (R. Guy et al., eds.), Gordon and Breach, New York, 1970.

T. Ahmed, Some new van der Waerden numbers and some van der Waerden-type numbers, Integers, 9 (2009), A06, 65-76.
T. Ahmed, On computation of exact van der Waerden numbers, Integers: Electronic Journal of Combinatorial Number Theory, 11 (2011), A71.
T. Ahmed, Some more Van der Waerden numbers, J. Int. Seq. 16 (2013) 13.4.4

Cf. A217005, A217007, A217008, A217059, A217060, A217236, A217237.

a(11)=55 added by Tanbir Ahmed, Dec 07 2012

A217037 Van der Waerden numbers w(2;5,n).

Original entry on oeis.org

178, 206, 260

Offset: 5

Tanbir Ahmed, Sep 24 2012

w(2;5,5)=178 (Stevens and Shantaram, 1978),w(2;5,6)=206 (Kouril, 2006), and w(2;5,7)=260 (Ahmed).

			w(2;5,5)=178.

M. Kouril, A Backtracking Framework for Beowulf Clusters with an Extension to Multi-Cluster Computation and Sat Benchmark Problem Implementation, Ph. D. Thesis, University of Cincinnati, Engineering: Computer Science and Engineering, 2006.

T. Ahmed, Some More van der Waerden Numbers
T. Ahmed, Some more Van der Waerden numbers, J. Int. Seq. 16 (2013) 13.4.4
R. Stevens and R. Shantaram, Computer-generated van der Waerden partitions, Math. Computation, 32 (1978), 635-636.

Cf. A171081, A171082.

A217007 Van der Waerden numbers w(j+2; t_0,t_1,...,t_{j-1}, 4, 4) with t_0 = t_1 = ... = t_{j-1} = 2.

Original entry on oeis.org

35, 40, 53, 54, 56, 66, 67

Offset: 0

Tanbir Ahmed, Sep 23 2012

			w(2;4,4)=35, w(3;2,4,4)=40, w(4:2,2,4,4)=53, and so on...

T. C. Brown, Some new van der Waerden numbers (preliminary report), Notices American Math. Society, 21 (1974), A-432.
V. Chvatal, Some unknown van der Waerden numbers, Combinatorial Structures and their Applications (R. Guy et al., eds.), Gordon and Breach, New York, 1970.

T. Ahmed, Some new van der Waerden numbers and some van der Waerden-type numbers, Integers, 9 (2009), A06, 65-76.
T. Ahmed, Some more Van der Waerden numbers, J. Int. Seq. 16 (2013) 13.4.4

Cf. A217005, A217008, A217058, A217059, A217060, A217236, A217237.

A217008 Van der Waerden numbers w(j+3; t_0,t_1,...,t_{j-1}, 3, 3, 3) with t_0 = t_1 = ... = t_{j-1} = 2.

Original entry on oeis.org

27, 40, 41, 42, 45, 49, 52

Offset: 0

Tanbir Ahmed, Sep 23 2012

			w(3;3,3,3)=27, w(4;2,3,3,3)=40, w(5;2,2,3,3,3)=41, and so on...

T. C. Brown, Some new van der Waerden numbers (preliminary report), Notices American Math. Society, 21 (1974), A-432.
V. Chvatal, Some unknown van der Waerden numbers, Combinatorial Structures and their Applications (R. Guy et al., eds.), Gordon and Breach, New York, 1970.

T. Ahmed, Some new van der Waerden numbers and some van der Waerden-type numbers, Integers, 9 (2009), A06, 65-76.
T. Ahmed, Some more Van der Waerden numbers, J. Int. Seq. 16 (2013) 13.4.4
B. Landman, A. Robertson, and C. Culver, Some new exact van der Waerden numbers, Integers, 5(2) (2005), A10.

Cf. A217005, A217007, A217058, A217059, A217060, A217236, A217237.

a(6)=52 added by Tanbir Ahmed, Dec 07 2012

A217005 Van der Waerden numbers w(j+2; t_0,t_1,...,t_{j-1}, 3, 3) with t_0 = t_1 = ... = t_{j-1} = 2.

Original entry on oeis.org

9, 14, 17, 20, 21, 24, 25, 28, 31, 33, 35, 37, 39, 42, 44, 46, 48, 50, 51

Offset: 0

Tanbir Ahmed, Sep 22 2012

			w(2;3,3)=9, w(3;2,3,3)=14, w(4;2,2,3,3)=17, and so on...

T. C. Brown, Some new van der Waerden numbers (preliminary report), Notices American Math. Society, 21 (1974), A-432.
V. Chvatal, Some unknown van der Waerden numbers, Combinatorial Structures and their Applications (R. Guy et al., eds.), Gordon and Breach, New York, 1970.

T. Ahmed, Some new van der Waerden numbers and some van der Waerden-type numbers, Integers, 9 (2009), A06, 65-76.
T. Ahmed, Some more Van der Waerden numbers, J. Int. Seq. 16 (2013) 13.4.4
B. Landman, A. Robertson, and C. Culver, Some new exact van der Waerden numbers, Integers, 5(2) (2005), A10.

Cf. A171081, A217007, A217008, A217058, A217059, A217060, A217236, A217237.

a(17)=50 and a(18)=51 added by Tanbir Ahmed, Dec 07 2012

cp's OEIS Frontend

User: Tanbir Ahmed

A217236 Van der Waerden numbers w(j+2; t_0,t_1,...,t_{j-1}, 4, 5) with t_0 = t_1 = ... = t_{j-1} = 2.

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A217237 Van der Waerden numbers w(j+2; t_0,t_1,...,t_{j-1}, 4, 6) with t_0 = t_1 = ... = t_{j-1} = 2.

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A217235 Van der Waerden numbers w(3; 3, 3, n).

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A217060 Van der Waerden numbers w(j+2; t_0,t_1,...,t_{j-1}, 3, 6) with t_0 = t_1 = ... = t_{j-1} = 2.

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A217059 Van der Waerden numbers w(j+2; t_0,t_1,...,t_{j-1}, 3, 5) with t_0 = t_1 = ... = t_{j-1} = 2.

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A217058 Van der Waerden numbers w(j+2; t_0,t_1,...,t_{j-1}, 3, 4) with t_0 = t_1 = ... = t_{j-1} = 2.

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A217037 Van der Waerden numbers w(2;5,n).

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A217007 Van der Waerden numbers w(j+2; t_0,t_1,...,t_{j-1}, 4, 4) with t_0 = t_1 = ... = t_{j-1} = 2.

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A217008 Van der Waerden numbers w(j+3; t_0,t_1,...,t_{j-1}, 3, 3, 3) with t_0 = t_1 = ... = t_{j-1} = 2.

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A217005 Van der Waerden numbers w(j+2; t_0,t_1,...,t_{j-1}, 3, 3) with t_0 = t_1 = ... = t_{j-1} = 2.

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