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

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

0,1

Comments

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.

References

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

Links

Table of n, a(n) for n=0..87.

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

Wikipedia, Benford's law.

Wikipedia, Zipf's law.

Formula

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

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A016556 A067050 A001355 * A105531 A369041 A129689

Adjacent sequences: A364852 A364853 A364854 * A364856 A364857 A364858

Keyword

nonn,base

Author

Marco Ripà, Aug 10 2023

Extensions

More terms from Jinyuan Wang, Aug 11 2023

Status

approved