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 A241299 Initial digit of the decimal expansion of n^(n^n) or n^^3 (in Don Knuth's up-arrow notation). 12
 0, 1, 1, 7, 1, 1, 2, 3, 6, 4, 1, 3, 4, 6, 1, 3, 1, 3, 1, 1, 3, 2, 3, 5, 5, 2, 2, 2, 8, 1, 1, 9, 1, 2, 3, 4, 8, 2, 4, 1, 1, 2, 8, 3, 2, 1, 4, 2, 5, 1, 6, 7, 2, 2, 2, 2, 2, 2, 8, 4, 1, 4, 8, 1, 5, 8, 4, 1, 4, 1, 2, 1, 9, 6, 6, 2, 1, 1, 7, 6, 1, 7, 7, 2, 4, 1, 8, 6, 1, 7, 1, 1, 3, 1, 2, 6, 3, 5, 1, 1, 1, 2, 2, 5, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS 0^^3 = 0 since 0^^k = 1 for even k, 0 for odd k, k >= 0. Conjecture: the distribution of the initial digits obey Zipf's law. The distribution of the first 1000 terms beginning with 1: 302, 196, 124, 91, 72, 46, 71, 53, 45. LINKS Robert P. Munafo and Robert G. Wilson v, Table of n, a(n) for n = 0..1000 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. Hans Havermann, Next 5 terms. 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 FORMULA For n > 0, a(n) = floor(t/10^floor(log_10(t))) where t = n^(n^n). a(n) = A000030(A002488). - Omar E. Pol, Jul 04 2019 EXAMPLE a(0) = 0, a(1) = 1, a(2) = 1 because 2^(2^2) = 16, a(3) = 7 because 3^(3^3) = 7625597484987 and its initial digit is 7, etc. MATHEMATICA g[n_] := Quotient[n^p, 10^(Floor[ p*Log10@ n] - (1004 + p))]; f[n_] := Block[{p = n}, Quotient[ Nest[ g@ # &, p, p], 10^(1004 + p)]]; Array[f, 105, 0] CROSSREFS Cf. A000030, A000312, A002488, A066022, A241291, A241292, A241293, A241294, A241295, A241296, A241297, A241298. Sequence in context: A317935 A115064 A086868 * A090269 A086867 A090266 Adjacent sequences:  A241296 A241297 A241298 * A241300 A241301 A241302 KEYWORD nonn,base,easy AUTHOR Robert Munafo and Robert G. Wilson v, Apr 18 2014 STATUS approved

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Last modified April 13 17:30 EDT 2021. Contains 342936 sequences. (Running on oeis4.)