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Nim-factorials: a(1)=1 and, for n>1, a(n)=n*a(n-1), where * denotes Nim multiplication.
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%I #15 Jun 10 2020 14:05:43

%S 1,2,1,4,2,11,1,8,5,9,2,4,9,4,1,16,8,140,5,82,9,145,2,44,6,108,9,154,

%T 13,209,1,32,20,132,10,243,172,123,4,139,68,62,11,222,182,92,2,16,36,

%U 224,5,242,91,24,11,105,178,56,5,241,92,205,1,64,39,20,23,161,225,53

%N Nim-factorials: a(1)=1 and, for n>1, a(n)=n*a(n-1), where * denotes Nim multiplication.

%C Conjectures:

%C (1) Nim-Factorial(2^n-1)=1 (verified for n=1,2,3,...,16).

%C (2) Nim-Factorial(2^n+2^(n-1)-1)=2 (verified for n=1,2,3,...,15).

%H Rémy Sigrist, <a href="/A059970/b059970.txt">Table of n, a(n) for n = 1..8192</a>

%H Rémy Sigrist, <a href="/A059970/a059970.gp.txt">PARI program for A059970</a>

%p A059970 := proc(n)

%p option remember;

%p if n =1 then

%p 1;

%p else

%p A051775(n,procname(n-1)) ;

%p end if;

%p end proc: # _R. J. Mathar_, Jul 28 2016 based on the program in b051775.txt

%o (PARI) See Links section.

%Y Cf. A058734, A006042, A051917.

%K nonn

%O 1,2

%A _John W. Layman_, Mar 05 2001

%E Corrected by _Gerald McGarvey_, Nov 12 2005