A342847 Value of r in best integer approximation r^s to n! with s >= r.

1, 1, 1, 2, 3, 2, 3, 4, 6, 5, 4, 7, 2, 5, 3, 4, 5, 11, 3, 6, 2, 11, 4, 3, 2, 14, 5, 12, 4, 14, 9, 18, 11, 17, 5, 24, 8, 12, 25, 28, 11, 26, 19, 14, 27, 12, 18, 5, 2, 34, 22, 32, 26, 9, 17, 29, 23, 12, 43, 6, 47, 4, 16, 32, 16, 4, 16, 30, 9, 12, 57, 37, 29, 28

Offset

0,4

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..73.

Sean A. Irvine, Java program (github)

Example

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

Crossrefs

Cf. A342848, A342849, A045772, A045773.

Sequence in context: A175266 A320053 A098235 * A345873 A114868 A249049

Adjacent sequences: A342844 A342845 A342846 * A342848 A342849 A342850

Keyword

nonn

Author

Sean A. Irvine, Mar 26 2021

Status

approved