A362004 - OEIS

%I #15 Feb 16 2025 08:34:05

%S 1,2,4,1,6,2,2

%N Initial digit of the decimal expansion of the tetration 2^^n (in Don Knuth's up-arrow notation).

%C The most significant digit of the base-10 representation of 2^(2^(2^...)) n times is given by floor(2^^n/10^(len(2^^n)-1)), where len(2^^n) indicates the number of digits of the argument.

%C Although it is known that 2^^6 starts with the digit 2 (see A241291), a(7) is not currently known (for details, see Googology link, section "First digits in tetration").

%H Googology, <a href="https://googology.fandom.com/wiki/Tetration">Tetration</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) = floor(2^^n/10^floor(log(2^^n))).

%e a(4) = 6, since 2^^4 = 65536.

%Y Cf. A241291, A241299, A244059.

%K base,hard,more,nonn

%O 0,2

%A _Marco Ripà_, Apr 02 2023