A364789 -id:A364789 - cp's OEIS frontend

A229522 Final digit (in decimal system) of (n^n)^n, i.e., (n^n)^n mod 10.

1, 6, 3, 6, 5, 6, 7, 6, 9, 0, 1, 6, 3, 6, 5, 6, 7, 6, 9, 0, 1, 6, 3, 6, 5, 6, 7, 6, 9, 0, 1, 6, 3, 6, 5, 6, 7, 6, 9, 0, 1, 6, 3, 6, 5, 6, 7, 6, 9, 0, 1, 6, 3, 6, 5, 6, 7, 6, 9, 0, 1, 6, 3, 6, 5, 6, 7, 6, 9, 0, 1, 6, 3, 6, 5, 6, 7, 6, 9, 0, 1, 6, 3, 6, 5, 6

Offset: 1

José María Grau Ribas, Sep 25 2013

Periodic sequence with period 10.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1).

Cf. A002489, A120962, A364789 (initial digit).

Mathematica
```
Table[PowerMod[n^n, n, 10], {n, 200}]
```

a(n)=n%=10; lift(Mod(n,10)^n^n) \\ Charles R Greathouse IV, Dec 27 2013

def A229522(n): return (0, 1, 6, 3, 6, 5, 6, 7, 6, 9)[n%10] # Chai Wah Wu, Aug 10 2023

a(n) = A120962(A002489(n)). - Michel Marcus, Aug 09 2023

A364837 Initial digit of 2^(2^n) = A001146(n).

Original entry on oeis.org

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

Offset: 0

Marco Ripà, Aug 10 2023

The sequence corresponds to the initial digit of 2vvn (since 2^(2^n) = ((((2^2)^2)^...)^2) (n times)), where vv indicates weak tetration (see links).
Conjecture: this sequence obeys Benford's law.
For any n > 1, the final digit of 2^(2^n) is 6.

			a(5) = 4, since 2^(2^5) = 2^32 = 4294967296.

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

Cf. A000030, A001146, A362004, A364789, A364855.

Join[{2},Table[Floor[2^(2^n)/10^Floor[Log10[2^(2^n)]]],{n,27}]] (* Stefano Spezia, Aug 10 2023 *)

def A364837(n): return int(str(1<<(1<Chai Wah Wu, Sep 14 2023

a(n) = floor(2^(2^n)/10^floor(log_10(2^(2^n)))), for n > 0.

a(n) = A000030(A001146(n)).

More terms from Jinyuan Wang, Aug 10 2023

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

A229522 Final digit (in decimal system) of (n^n)^n, i.e., (n^n)^n mod 10.

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A364837 Initial digit of 2^(2^n) = A001146(n).

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

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