A395131 Number of occurrences of digit n in 9^9^9.

36967783, 36967842, 36969142, 36973760, 36979528, 36961052, 36966895, 36972157, 36970838, 36964103

Offset

0,1

Comments

In 1979, Joseph Madachy predicted in Madachy's Mathematical Recreations that the 369693100 digits of 9^9^9 "would almost guarantee that the number never will be fully evaluated." Now any home computer can calculate it in seconds.

9^9^9 = 3^774840978, so a surplus of 3s in the digit distribution might at first glance be expected. In fact, each digit count differs by less than 0.03% from the mean.

At 12 digits per inch (about 4.7 per cm), the decimal expansion of 9^9^9 printed on a paper tape would exceed 486 miles (782 km).

References

J. S. Madachy, Madachy's Mathematical Recreations, Dover Publications, New York, 1979, p. 176.

Links

Table of n, a(n) for n=0..9.

Wikipedia, Joseph Madachy.

Example

a(8)=36970838 because the digit 8 appears 36970838 times in 9^9^9.

Mathematica

Last/@Sort[Tally[IntegerDigits[9^9^9]]]
(* 9^9^9 takes 6 seconds; IntegerDigits 120 seconds; Tally 1 second *)

Crossrefs

Cf. A054382, A241298, A002488.

Sequence in context: A346285 A364704 A028965 * A273508 A340713 A263347

Adjacent sequences: A395128 A395129 A395130 * A395132 A395133 A395134

Keyword

nonn,base,fini,full

Author

David Dewan, Apr 12 2026

Status

approved