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

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, 13, 209, 1, 32, 20, 132, 10, 243, 172, 123, 4, 139, 68, 62, 11, 222, 182, 92, 2, 16, 36, 224, 5, 242, 91, 24, 11, 105, 178, 56, 5, 241, 92, 205, 1, 64, 39, 20, 23, 161, 225, 53

Offset: 1

Author

John W. Layman, Mar 05 2001

Keywords

• nonn

Comments

Conjectures:

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

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

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8192
• Rémy Sigrist, PARI program for A059970

Crossrefs

Cf. A058734, A006042, A051917.

Programs

Maple

A059970 := proc(n)
    option remember;
    if n =1 then
        1;
    else
        A051775(n,procname(n-1)) ;
    end if;
end proc: # R. J. Mathar, Jul 28 2016 based on the program in b051775.txt

PARI

\\ See Links section.

Extensions

Corrected by Gerald McGarvey, Nov 12 2005