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Number of impartial misere games born on or before day n.
5

%I #42 Sep 17 2023 20:39:57

%S 1,2,3,5,22,4171780

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

%C 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").

%C "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.

%C 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

%D J. H. Conway, On Numbers and Games, pp. 139-140.

%D Aaron N. Siegel, Combinatorial Game Theory, AMS Graduate Texts in Mathematics Vol 146 (2013), p. 248.

%H Steven Finch, <a href="https://doi.org/10.1007/s00283-021-10060-2">The On-Line Encyclopedia of Integer Sequences, founded in 1964 by N. J. A. Sloane</a>, A Tribute to John Horton Conway, The Mathematical Intelligencer (2021) Vol. 43, 146-147.

%H Chris Thompson, <a href="https://groups.google.com/d/msg/sci.math/IrjOWJ5PrwI/m9hGuvYCmUoJ">Count of day 6 misere-inequivalent impartial games</a>, Usenet article, February 1999.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Mis%C3%A8re#Mis.C3.A8re_game">Misère: Misère game</a>

%Y Cf. A037142.

%K nice,nonn

%O 0,2

%A _N. J. A. Sloane_