A342849 Value of n!-r^s in best integer approximation r^s to n! with s >= r.

0, 0, 1, 2, -3, -8, -9, 944, -6336, -27745, -565504, -436807, -57869312, 123505175, -6964887627, 208162740224, 1849303559875, -24062405487241, 843313139172477, -9976603433435136, 127058998962946048, -10068148276705106291, -56590892939803623424

Offset

0,4

Comments

The best approximation can be smaller or larger than n!; that is, minimize abs(n!-r^s).

Links

Table of n, a(n) for n=0..22.

Example

a(4) = 3, since 3^3 - 3 = 24 = 4! (note 5^2-1 = 24 is not allowed because 2 < 5).
a(7) = 944, since 4^6 + 944 = 5040 = 7! and there is no closer approximation.

Crossrefs

Cf. A342847, A342848, A045772, A045773.

Sequence in context: A364382 A133165 A019307 * A247580 A345352 A028742

Adjacent sequences: A342846 A342847 A342848 * A342850 A342851 A342852

Keyword

sign

Author

Sean A. Irvine, Mar 26 2021

Status

approved