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

1, 1, 4, 7, 2

Offset: 0

Author

Marco Ripà, Jun 19 2023

Keywords

• base
• hard
• more
• nonn

Comments

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.

Examples

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

Links

• 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.

Crossrefs

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

Cf. A241299, A244059, A362004.

Formula

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

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