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 1-5 of 5 results.

A037142 Erroneous version of A047995: Number of impartial misere games born on or before day n.

Original entry on oeis.org

1, 4, 22, 4171780
Offset: 0

Views

Author

Jeffrey Harris (alvinharris(AT)home.com)

Keywords

Comments

Apparently a conflation of A047995 (impartial games, misere play) and A065401 (partisan games, normal play) based on the (surely?) accidental appearance of 22 in both sequences. - Christopher E. Thompson, Nov 17 2015

Crossrefs

Cf. A047995, A065401.

Formula

gamma(0) = 0.149027998351785...; gamma(n+1) = (2^gamma(n)); f(n) = ceiling(gamma(n)).

Extensions

Next term = (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.
Probably this is an incorrect version of A047995. - N. J. A. Sloane

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.

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.

A368588 Number of misère-play left dead end games born by day n.

Original entry on oeis.org

1, 2, 4, 10, 52, 21278
Offset: 0

Views

Author

Aaron N. Siegel, Dec 31 2023

Keywords

Comments

A partizan combinatorial game G is a left dead end if no subposition of G has any left options. In normal play, every left dead end is equal to a nonpositive integer. In misère play, the left dead ends have a more intricate structure; this sequence counts the misère-inequivalent left dead ends with birthday <= n.

References

  • E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982.

Links

Crossrefs

Cf. A065401, A047995, A260969.
Showing 1-5 of 5 results.

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

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