A392143 a(n) = (n^(n - 1) - 1)^n.

0, 1, 512, 15752961, 94606929690624, 220903392825527587890625, 311954920641940794545461153939587072, 374142991911400415397080306521056997980469670707201, 507528679944764261210790982765425081637339300928309681979392000000000, 999999990000000044999999880000000209999999748000000209999999880000000044999999990000000001

Offset

1,3

Comments

For n > 3, a(n) = (n^(n - 1) - 1)^n is a perfect power of exact order n (by Mihailescu's theorem).

For the number of stable digits of the tetration a(n)^^b (b > 0 integer), in the radix-n numeral system, see Identity (5) in "Universal +-1 congruence speed invariant in any numeral system" (in Links).

Links

Table of n, a(n) for n=1..10.

Marco Ripà, On the relation between perfect powers and tetration frozen digits, Journal of AppliedMath, 2024, 2(5), 1771.

Marco Ripà, Radix-r Congruence Speed Verification Tool (Python Script), Zenodo, 2025.

Marco Ripà, Universal +-1 congruence speed invariant in any numeral system, Zenodo, 2025.

Marco Ripà and Gabriele Di Pietro, A Compact Notation for Peculiar Properties Characterizing Integer Tetration, Zenodo, 2025.

Formula

a(n) = (n^(n-1)-1)^n = (n^n-n)^n/n^n.

Example

For n = 3, a(3) = (3^(3 - 1) - 1)^2 = (9 - 1)^3 = 512.

Mathematica

Table[(n^(n-1)-1)^n, {n, 1, 9}]

Crossrefs

Cf. A253604, A373387, A390597.

Sequence in context: A283935 A016833 A103352 * A013848 A227607 A016881

Adjacent sequences: A392140 A392141 A392142 * A392144 A392145 A392146

Keyword

nonn,easy

Author

Marco Ripà, Jan 01 2026

Status

approved