A244059 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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

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.

Eric Weisstein's World of Mathematics, Joyce Sequence

Wikipedia, Zipf'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. A324220 (number of digits).

KEYWORD

nonn,base,hard,more

AUTHOR

STATUS

approved