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.

A065401 Number of normal play partisan games born on or before day n.

Original entry on oeis.org

1, 4, 22, 1474
Offset: 0

Views

Author

R. K. Guy, Nov 23 2001

Keywords

Comments

Fraser and Wolfe prove upper and lower bounds on a(n+1) in terms of a(n). In particular they give the (probably quite weak) lower bound of 3*10^12 for a(4). - Christopher E. Thompson, Aug 06 2015

References

  • Dan Calistrate, Marc Paulhus and David Wolfe, On the lattice structure of finite games, in More Games of No Chance (Berkeley, CA, 2000), Math. Sci. Res. Inst. Publ., 42, Cambridge Univ. Press, Cambridge, 2002, pp. 25-30.
  • J. H. Conway, On Numbers and Games, Academic Press, NY, 1976.
  • Aaron N. Siegel, Combinatorial Game Theory, AMS Graduate Texts in Mathematics Vol 146 (2013), p. 158.

Links

Crossrefs

Cf. A065402, A065407, A047995, A037142, A114561, A125990, A126011.

Formula

a(n) = A125990(2*A114561(n)). - Antti Karttunen, Oct 18 2018

Extensions

Dean Hickerson and Robert Li found a(3) in 1974.

A047995 Number of impartial misere games born on or before day n.

Original entry on oeis.org

1, 2, 3, 5, 22, 4171780
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

Next term = 2^4171780 - 2^2096640 - 2^2095104 - 2^2094593 - 2^2094080 - 3.2^2091522 - 2^2088960 - 2^2088705 - 2^2088448 - 2^2088193 - 2^2086912 - 2^2086657 - 2^2086401 - 2^2086145 - 2^2085888 - 2^2079234 + 2^1960962 + 21 (Christopher E. Thompson, who remarks that this term is given incorrectly in "On Numbers and Games").
"On Numbers and Games" incorrectly states that the next term is 2^4171780 - 2^2095104 - 3*2^2094593 - 2^2094081 - 3*2^2091522 - 2^2088960 - 3*2^2088448 - 2^2087937 - 2^2086912 - 2^2086657 - 2^2086401 - 2^2086145 - 2^2085888 - 2^2079234 + 2^1960962 + 21.
Aaron Siegel reports (see references) that he and Dan Hoey jointly verified the revised value of the Next term [i.e., a(6)] above. - Christopher E. Thompson, Oct 21 2015

References

  • J. H. Conway, On Numbers and Games, pp. 139-140.
  • Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 6.11.1, p. 451.
  • Aaron N. Siegel, Combinatorial Game Theory, AMS Graduate Texts in Mathematics Vol 146 (2013), p. 248.

Links

Crossrefs

Cf. A037142.

A065402 Number of normal play partisan games born on day n.

Original entry on oeis.org

1, 3, 18, 1452
Offset: 0

Views

Author

R. K. Guy, Nov 23 2001

Keywords

Comments

Dean Hickerson and Robert Li found a(3) in 1974.

Examples

			Day 0: 0; day 1: 1 -1 *; day 2, 18: 2 -2 1/2 -1/2 1* -1* +/-1 up upstar down downstar *2 1|* 1|0 1|0,* *|-1 0|-1 0,*|-1.

References

  • Dan Calistrate, Marc Paulhus and David Wolfe, On the lattice structure of finite games, in More Games of No Chance (Berkeley, CA, 2000), Math. Sci. Res. Inst. Publ., 42, Cambridge Univ. Press, Cambridge, 2002, pp. 25-30.
  • J. H. Conway, On Numbers and Games, Academic Press, NY, 1976.

Crossrefs

Cf. A065401, A065407, A047995, A037142.

A065407 Number of levels in lattice formed by normal play partisan games born on day n.

Original entry on oeis.org

1, 3, 9, 45, 2949
Offset: 0

Views

Author

R. K. Guy, Nov 23 2001

Keywords

References

  • Dan Calistrate, Marc Paulhus and David Wolfe, On the lattice structure of finite games, in More Games of No Chance (Berkeley, CA, 2000), Math. Sci. Res. Inst. Publ., 42, Cambridge Univ. Press, Cambridge, 2002, pp. 25-30.

Crossrefs

Cf. A065401, A065402, A047995, A037142. Equals 2*A065402(n-1) + 1.
Showing 1-4 of 4 results.

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

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