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

Offset: 1

Author

Robert G. Wilson v, Aug 30 2014

Keywords

• nonn
• base

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

Crossrefs

Cf. A241293, A241299, A244059.

Programs

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]

Formula

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