A246564 - OEIS

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A246564

The n-th least-significant decimal digit of n^^n (in Don Knuth's up-arrow notation).

1, 0, 9, 2, 0, 2, 5, 3, 3, 0, 7, 8, 5, 6, 6, 7, 8, 3, 1, 0, 1, 7, 8, 8, 7, 8, 6, 2, 4, 0, 9, 8, 0, 3, 0, 3, 5, 6, 7, 0, 6, 5, 2, 0, 1, 0, 7, 5, 3, 0, 2, 9, 5, 8, 3, 6, 8, 7, 0, 0, 7, 3, 7, 3, 0, 8, 4, 0, 8, 0, 7, 6, 8, 0, 3, 0, 6, 7, 1, 0, 7, 7, 2, 8, 5, 7, 9, 7, 3, 0, 0, 9, 3, 6, 6, 3, 4, 2, 1, 0, 5, 9, 8, 8, 6

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OFFSET

1,3

COMMENTS

This sequence was inspired by the 41st Wohascum County problem.

The distribution of the first 500 terms beginning with 0: 101, 43, 40, 42, 29, 49, 43, 53, 58, 42.

The distribution does not conform to Benford's / Zipf's law, but seems to be evenly distributed once multiples of ten are excluded.

REFERENCES

George T. Gilbert, Mark I. Krusemeyer and Loren C. Larson, The Wohascum County Problem Book, The Mathematical Association of America, Dolciani Mathematical Expositions No. 14, 1993, problem 41 "What is the fifth digit from the end (the ten thousands digit) of the number 5^5^5^5^5?", page 11 and solution on page 76.

Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Robert P. Munafo, Sequence A094358, 2^^N = 1 mod N.

Robert P. Munafo, Hyper4 Iterated Exponential Function.

Robert G. Wilson v, Mathematica coding for "SuperPowerMod" from Vardi.

Wikipedia, Knuth's up-arrow notation.

Index entries for sequences related to Benford's law

FORMULA

if n (mod 10) == 0 then a(n) = 0.

MATHEMATICA

(* first load "SuperPowerMod" from Vardi, see link above, and then *) f[n_] := Quotient[ SuperPowerMod[ n, n, 10^n], 10^(n - 1)]; Array[f, 105]