A364789 Initial digit of (n^n)^n (A002489(n)).

1, 1, 1, 1, 4, 2, 1, 2, 6, 1, 1, 1, 2, 1, 4, 4, 1, 3, 5, 4, 2, 1, 5, 2, 1, 5, 3, 2, 3, 7, 2, 1, 1, 4, 2, 3, 9, 7, 1, 1, 1, 1, 2, 1, 5, 5, 2, 4, 3, 1, 2, 2, 1, 3, 4, 3, 2, 6, 1, 2, 2, 1, 8, 3, 1, 3, 8, 1, 3, 5, 9, 1, 2, 4, 8, 1, 3, 1, 3, 1, 5, 3, 3, 3, 5, 1, 3

Offset

0,5

Comments

a(0) = 1 is from (0^0)^0 = 1 per A002489.

The author conjectures that this sequence obeys the well-known Benford's law.

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Pointless Large numbers stuff by Cookiefonster, 2.03 The Weak Hyper-Operators.

Wikipedia, Benford's law.

Formula

a(n) = floor(((n^n)^n)/10^floor(log_10((n^n)^n))).

a(n) = A000030(A002489(n)).

Example

a(4) = 4, since (4^4)^4 = 4^(4^2) = 4294967296.

Mathematica

A364789[n_] := If[n == 0, 1, First[IntegerDigits[(n^n)^n]]];
Array[A364789, 100, 0] (* Paolo Xausa, Jan 31 2024 *)

Prog

(Python)
def A364789(n): return int(str((n**n)**n)[0]) # Chai Wah Wu, Aug 10 2023

Crossrefs

Cf. A000030, A002489, A241299, A363746, A364837, A364855.

Cf. A229522 (final digit).

Sequence in context: A132116 A327252 A229974 * A281065 A280988 A175665

Adjacent sequences: A364786 A364787 A364788 * A364790 A364791 A364792

Keyword

base,easy,nonn

Author

Marco Ripà, Aug 08 2023

Status

approved