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

1, 2, 3, 5, 22, 4171780

Offset

0,2

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

Table of n, a(n) for n=0..5.

Steven Finch, The On-Line Encyclopedia of Integer Sequences, founded in 1964 by N. J. A. Sloane, A Tribute to John Horton Conway, The Mathematical Intelligencer (2021) Vol. 43, 146-147.

Chris Thompson, Count of day 6 misere-inequivalent impartial games, Usenet article, February 1999.

Wikipedia, Misère: Misère game.

Crossrefs

Cf. A037142.

Sequence in context: A093499 A339228 A013639 * A244862 A373794 A338403

Adjacent sequences: A047992 A047993 A047994 * A047996 A047997 A047998

Keyword

nice,nonn

Author

N. J. A. Sloane

Status

approved