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

Author

Simon R Blow, Aug 07 2023

Keywords

• nonn
• base

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.

Examples

			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.

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