A362004 -id:A362004 - cp's OEIS frontend

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

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

A363746 Initial digit of the decimal expansion of the tetration n^^n (in Don Knuth's up-arrow notation).

Original entry on oeis.org

1, 1, 4, 7, 2

Offset: 0

Marco Ripà, Jun 19 2023

a(5), the most significant digit of the tetration 5^^5, has been estimated to be equal to 1 (and this is also consistent with Benford's law), but there is not any strict proof at the present time and computers are not powerful enough to calculate it without uncertainty.

			a(3) = 7 since 3^^3 = 7625597484987.

Allam's Numbers, Digits of tetrational numbers
A. Bogomolny, Benford's Law and Zipf's Law, Cut the Knot.org.
Googology, Tetration.
Eric Weisstein's World of Mathematics, Joyce Sequence.
Wikipedia, Knuth's up-arrow notation.

Cf. A000030, A004231 (n^^n), A241293 (4^^4 digits).

Cf. A241299, A244059, A362004.

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

a(n) = A000030(A004231(n)).

cp's OEIS Frontend

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

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