A395696 - OEIS

%I #13 May 19 2026 16:46:58

%S 1,3,2,7,1

%N Initial digit of the decimal expansion of the tetration 3^^n.

%C 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).

%H Googology, <a href="https://googology.fandom.com/wiki/Tetration">Tetration</a>.

%H Googology, <a href="https://googology.fandom.com/wiki/User:Allam948736">Googology User Allam948736</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PowerTower.html">Power Tower</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation">Knuth's up-arrow notation</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tetration">Tetration</a>.

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

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

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

%K base,hard,more,nonn

%O 0,2

%A _Marco Ripà_, May 03 2026