A362004 Initial digit of the decimal expansion of the tetration 2^^n (in Don Knuth's up-arrow notation).

1, 2, 4, 1, 6, 2, 2

Offset: 0

Author

Marco Ripà, Apr 02 2023

Keywords

• base
• hard
• more
• nonn

Comments

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.

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").

Examples

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

Links

• Googology, Tetration.
• Eric Weisstein's World of Mathematics, Power Tower
• Wikipedia, Knuth's up-arrow notation
• Wikipedia, Tetration

Crossrefs

Cf. A241291, A241299, A244059.

Formula

a(n) = floor(2^^n/10^floor(log(2^^n))).