games born on day n

[Richard Guy]

Yes, it's not the same.  These are the (general)
partizan games:

day 0    0

day 1    0  *  1  -1

day 2    22 games including the above and
         up, down, upstar, downstar, pm1, 1*
         etc, etc.     R.

On Wed, 21 Nov 2001, N. J. A. Sloane wrote:

> Richard,
> 
> I take it that that's not the same as this sequence?
> 
> %I A037142
> %S A037142 1,4,22,4171780
> %N A037142 Number of impartial misere games born on or before day n.
> %D A037142 J. H. Conway, On Numbers and Games, pp. 139-140.
> %F A037142 gamma(0)=0.149027998351785...; gamma(n+1)=(2^gamma(n)); f(n)=ceiling(gamma(n))
> %K A037142 huge,nonn
> %O A037142 0,2
> %A A037142 Jeffrey Harris (alvinharris at home.com)
> %E A037142 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.
> %E A037142 Probably this is an incorrect version of A047995 - njas.
> 
> 
> which is in turn an incorrect version of
> 
> %I A047995
> %S A047995 1,2,3,5,22,4171780
> %N A047995 Number of impartial misere games born on or before day n.
> %D A047995 J. H. Conway, On Numbers and Games, pp. 139-140.
> %Y A047995 Cf. A037142.
> %K A047995 huge,nice,nonn
> %O A047995 0,2
> %A A047995 njas
> %E A047995 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 (Chris Thompson, cet1 at c
> %E A047995 "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 + 2^1960
> 
> NJAS
> 
> You said:
> 1 4 22 1474
> ....
> 
>