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

0,3

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.

Links

Table of n, a(n) for n=0..4.

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.

Formula

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

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

Example

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

Crossrefs

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

Cf. A241299, A244059, A362004.

Sequence in context: A289523 A078220 A256040 * A257817 A246710 A139346

Adjacent sequences: A363743 A363744 A363745 * A363747 A363748 A363749

Keyword

base,hard,more,nonn

Author

Marco Ripà, Jun 19 2023

Status

approved