A066908 n^n minus largest factorial less than or equal to n^n.

0, 0, 2, 3, 136, 2405, 6336, 460663, 13148416, 347503689, 3772979200, 198133379411, 7608426080256, 281952316704253, 4709633119830016, 316248789972027375, 16013842065532911616, 776149319714627324177

Offset

0,3

Comments

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.

Links

Table of n, a(n) for n=0..17.

sci.math discussion

Formula

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

Example

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

Crossrefs

Cf. A000142, A000312, A064318.

Sequence in context: A007608 A010343 A118169 * A057738 A234999 A254787

Adjacent sequences: A066905 A066906 A066907 * A066909 A066910 A066911

Keyword

nonn

Author

Henry Bottomley, Jan 22 2002

Status

approved