A364786 We exclude powers of 10 and numbers of the form 11...111 in which the number of 1's is a power of 10. Then a(n) is the smallest number (not excluded) whose trajectory under iteration of "x -> sum of n-th powers of digits of x" reaches 1.

19, 7, 112, 11123, 1111222, 111111245666689, 1111133333333335, 1111122333333333333333333346677777777888, 22222222222222222226666668888888, 233444445555555555555555555555555555555555555555555577, 1222222222233333333333333444444444455555555555555556666666666666666666666677778888889

Offset

1,1

Comments

For n!=2, it appears that the first step in the trajectory is always to a power of 10, so that the task would be to find the shortest and lexicographically smallest partition of a power of 10 into parts 1^n,...,9^n.

Links

Table of n, a(n) for n=1..11.

Example

a(1) = 19 since 1^1 + 9^1 = 10 and 1^1 + 0^1 = 1.
a(3) = 112 since 1^3 + 1^3 + 2^3 = 10 and 1^3 + 0^3 = 1.

Crossrefs

Cf. A007770, A035497, A046519.

Sequence in context: A185424 A040347 A040346 * A124608 A218162 A064264

Adjacent sequences: A364783 A364784 A364785 * A364787 A364788 A364789

Keyword

nonn,base

Author

Simon R Blow, Aug 07 2023

Extensions

a(6), a(8), and a(9) corrected by, and a(10) and a(11) from Jon E. Schoenfield, Aug 10 2023

Definition clarified by N. J. A. Sloane, Sep 15 2023

Status

approved