A244059 Initial digit of the decimal expansion of n^(n^(n^n)) or n^^4 (in Don Knuth's up-arrow notation).

1, 1, 6, 1, 2, 1, 4, 7, 6, 2, 1

Offset: 0

Author

Robert Munafo and Robert G. Wilson v, Jun 18 2014

Keywords

• nonn
• base
• hard
• more

Comments

This sequence can also be written as (n↑↑4) in Knuth up-arrow notation.

0^^4 = 1 since 0^^k = 1 for even k, 0 for odd k, k >= 0.

Conjecture: the distribution of the initial digits obey G. K. Zipf's law.

Examples

			a(4)=2 because A241293(1)=2.
		

Links

• Cut the Knot.org, Benford's Law and Zipf's Law, A. Bogomolny, Zipf's Law, Benford's Law from Interactive Mathematics Miscellany and Puzzles.
• M. E. J. Newman, Power laws, Pareto distributions and Zipf's law.
• Eric Weisstein's World of Mathematics, Joyce Sequence
• Wikipedia, Knuth's up-arrow notation
• Wikipedia, Zipf's law
• Index entries for sequences related to Benford's law

Crossrefs

Cf. A241291, A241292, A241293, A241294, A241295, A241296, A241297, A243913, A241299.

Cf. A324220 (number of digits).

Programs

PARI

a(n)=digits(n^n^n^n)[1] \\ impractical for large n; Charles R Greathouse IV, May 13 2015