A364837 -id:A364837 - cp's OEIS frontend

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

Marco Ripà, Aug 08 2023

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

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

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

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.

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

Cf. A229522 (final digit).

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

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

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

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

A364855 Initial digit of 3^(3^n) (A055777(n)).

Original entry on oeis.org

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

Offset: 0

Marco Ripà, Aug 10 2023

This sequence corresponds to the initial digit of 3vvn (since 3^(3^n) = ((((3^3)^3)^...)^3) n-times), where vv indicates weak tetration (see links).
The author conjectures that the distribution of the initial digits of the present sequence obey Benford's law or Zipf's law (see links).
The corresponding final digit of 3^(3^n) is A010705(n) = 3 if n even or 7 if n odd.

			a(2) = 1, since 3^(3^2) = 3^9 = 19683.

A. Iorliam, Natural Laws (Benford's Law and Zipf's Law) For Network Traffic Analysis, In: Cybersecurity in Nigeria. SpringerBriefs in Cybersecurity. Springer, Cham (2019), 3-22. DOI: 10.1007/978-3-030-15210-9_2

Pointless Large numbers stuff by Cookiefonster, 2.03 The Weak Hyper-Operators.
Wikipedia, Benford's law.
Wikipedia, Zipf's law.

Cf. A000030, A010705 (last digit), A055777, A364789, A364837.

Join[{3},Table[Floor[3^(3^n)/10^Floor[Log10[3^(3^n)]]],{n,16}]]

a(n) = floor(3^(3^n)/10^floor(log_10(3^(3^n)))).

a(n) = A000030(A055777(n)).

More terms from Jinyuan Wang, Aug 11 2023

cp's OEIS Frontend

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

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