A246605 Numbers n such that n = (digital root of n)^(number of digits of n).

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 81, 512, 729, 2401, 6561, 32768, 59049, 531441, 2097152, 4782969, 43046721, 134217728, 387420489, 3486784401, 31381059609, 282429536481, 2541865828329, 22876792454961, 205891132094649, 1853020188851841, 16677181699666569, 150094635296999121, 1350851717672992089, 12157665459056928801, 109418989131512359209

Offset: 0

Author

Ivan N. Ianakiev, Aug 31 2014

Keywords

• base
• nonn
• fini
• full

Comments

This is a supersequence of A038178. Its finiteness stems from the fact that the number of digits of (digital root(x))^y is less than y, for every y > 21.

Examples

			a(10) = 81 = 9^2 = A010888(81)^A055642(81).
		

Links

• Ivan N. Ianakiev, Table of n, a(n) for n = 0..34

Crossrefs

Cf. A010888, A055642, A038178.

Programs

Mathematica

lst={0,1,2,3,4,5,6};Do[If[7^n==Mod[7^n,9]^n,AppendTo[lst,7^n]],{n,1,9}];Do[If[8^n==Mod[8^n,9]^n,AppendTo[lst,8^n]],{n,1,9}];Union[Join[lst,Table[9^x,{x,1,21}]]]