A395696 Initial digit of the decimal expansion of the tetration 3^^n.

1, 3, 2, 7, 1

Offset

0,2

Comments

a(n) is the leading (decimal) digit of 3^^n, and thus the term a(5) is currently out of computational reach, as it would require evaluating the fractional part of 3^^4*log_10(3) with extremely high precision (see the Googology User's page "Allam948736", in Links, for a related discussion, where the author specifies that 3^^5 has about 6.00225*10^3638334640023 decimal digits).

Links

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

Googology, Tetration.

Googology, Googology User Allam948736.

Eric Weisstein's World of Mathematics, Power Tower.

Wikipedia, Knuth's up-arrow notation.

Wikipedia, Tetration.

Formula

a(n) = A000030(3^^n).

Example

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

Crossrefs

Cf. A000030, A241291, A241299, A244059, A255820, A362004.

Sequence in context: A019951 A019971 A330501 * A010606 A348493 A317919

Adjacent sequences: A395693 A395694 A395695 * A395697 A395698 A395699

Keyword

base,hard,more,nonn

Author

Marco Ripà, May 03 2026

Status

approved