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n^n minus largest factorial less than or equal to n^n.
0

%I #3 Mar 30 2012 18:51:35

%S 0,0,2,3,136,2405,6336,460663,13148416,347503689,3772979200,

%T 198133379411,7608426080256,281952316704253,4709633119830016,

%U 316248789972027375,16013842065532911616,776149319714627324177

%N n^n minus largest factorial less than or equal to n^n.

%C Although this appears to be increasing rapidly and monotonically, Dave Rusin showed in the usenet discussion that a(4581631) is less than a(4581630): a(4581631)=4581631^4581631-4879731! is less than 8*10^30518328 while a(4581630) is just over 10^30518329.

%H <a href="http://groups.google.com/groups?threadm=b4be2fdf.0201101751.46f8a641%40posting.google.com">sci.math discussion</a>

%F a(n)=n^n-A064318(n)!

%e a(4)=136 since 4^4=256, the largest factorial less than or equal to 256 is 5!=120 and 256-120=136

%Y Cf. A000142, A000312, A064318.

%K nonn

%O 0,3

%A _Henry Bottomley_, Jan 22 2002