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A059970 Nim-factorials: a(1)=1 and, for n>1, a(n)=n*a(n-1), where * denotes Nim multiplication.

%I A059970 #19 Mar 24 2025 22:34:29
%S A059970 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 A059970 13,209,1,32,20,132,10,243,172,123,4,139,68,62,11,222,182,92,2,16,36,
%U A059970 224,5,242,91,24,11,105,178,56,5,241,92,205,1,64,39,20,23,161,225,53
%N A059970 Nim-factorials: a(1)=1 and, for n>1, a(n)=n*a(n-1), where * denotes Nim multiplication.
%C A059970 Conjectures:
%C A059970 (1) Nim-Factorial(2^n-1)=1 (verified for n=1,2,3,...,16).
%C A059970 (2) Nim-Factorial(2^n+2^(n-1)-1)=2 (verified for n=1,2,3,...,15).
%H A059970 Rémy Sigrist, <a href="/A059970/b059970.txt">Table of n, a(n) for n = 1..8192</a>
%H A059970 Rémy Sigrist, <a href="/A059970/a059970.gp.txt">PARI program for A059970</a>
%p A059970 A059970 := proc(n)
%p A059970     option remember;
%p A059970     if n =1 then
%p A059970         1;
%p A059970     else
%p A059970         A051775(n,procname(n-1)) ;
%p A059970     end if;
%p A059970 end proc: # _R. J. Mathar_, Jul 28 2016 based on the program in b051775.txt
%o A059970 (PARI) \\ See Links section.
%Y A059970 Cf. A058734, A006042, A051917.
%K A059970 nonn
%O A059970 1,2
%A A059970 _John W. Layman_, Mar 05 2001
%E A059970 Corrected by _Gerald McGarvey_, Nov 12 2005