

A246564


The nth leastsignificant decimal digit of n^^n (in Don Knuth's uparrow notation).


1



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," AddisonWesley Publishing Co., Redwood City, CA, 1991, pages 226229.


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 P. Munafo and Kenny TM Chan, Hypercalc
Robert G. Wilson v, Mathematica coding for "SuperPowerMod" from Vardi.
Wikipedia, Knuth's uparrow 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]


CROSSREFS

Cf. A241293, A241299, A244059.
Sequence in context: A046761 A335539 A193373 * A327995 A019876 A155696
Adjacent sequences: A246561 A246562 A246563 * A246565 A246566 A246567


KEYWORD

nonn,base


AUTHOR

Robert G. Wilson v, Aug 30 2014


STATUS

approved



