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

0,3

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.

Links

Table of n, a(n) for n=0..10.

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

Example

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

Prog

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

Crossrefs

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

Cf. A324220 (number of digits).

Sequence in context: A085552 A002950 A324046 * A121090 A321991 A010135

Adjacent sequences: A244056 A244057 A244058 * A244060 A244061 A244062

Keyword

nonn,base,hard,more

Author

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

Status

approved