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

Author

Marco Ripà, Aug 10 2023

Keywords

• nonn
• base

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.

Examples

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

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

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

Crossrefs

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

Programs

Mathematica

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

Formula

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

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

Extensions

More terms from Jinyuan Wang, Aug 11 2023