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A246564
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The n-th least-significant decimal digit of n^^n (in Don Knuth's up-arrow notation).
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1
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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
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1,3
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COMMENTS
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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.
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REFERENCES
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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.
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LINKS
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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 P. Munafo and Kenny T-M Chan, Hypercalc
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
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FORMULA
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if n (mod 10) == 0 then a(n) = 0.
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MATHEMATICA
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(* first load "SuperPowerMod" from Vardi, see link above, and then *) f[n_] := Quotient[ SuperPowerMod[ n, n, 10^n], 10^(n - 1)]; Array[f, 105]
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CROSSREFS
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Cf. A241293, A241299, A244059.
Sequence in context: A258437 A046761 A193373 * A327995 A019876 A155696
Adjacent sequences: A246561 A246562 A246563 * A246565 A246566 A246567
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KEYWORD
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nonn,base
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AUTHOR
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Robert G. Wilson v, Aug 30 2014
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STATUS
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approved
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