A342848 Value of s in best integer approximation r^s to n! with s >= r.

1, 1, 2, 2, 3, 7, 6, 6, 6, 8, 11, 9, 29, 14, 23, 20, 19, 14, 33, 22, 61, 19, 35, 47, 79, 22, 38, 26, 49, 27, 34, 27, 34, 30, 55, 29, 46, 40, 32, 32, 46, 35, 40, 46, 38, 52, 46, 85, 203, 41, 48, 44, 48, 73, 58, 50, 55, 71, 48, 103, 49, 139, 71, 58, 74, 151, 77

Offset

0,3

Comments

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

In the case of a tie, choose the smallest possible s (for example, when n=3, n!=6, we have 2^2 <= 6 <= 2^3 equally distant, choose 2^2).

Links

Table of n, a(n) for n=0..66.

Example

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

Crossrefs

Cf. A342847, A342849, A045772, A045773.

Sequence in context: A051301 A002583 A068519 * A339826 A108041 A259254

Adjacent sequences: A342845 A342846 A342847 * A342849 A342850 A342851

Keyword

nonn

Author

Sean A. Irvine, Mar 26 2021

Status

approved