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

0,3

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.

Links

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

Example

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

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}]]]

Crossrefs

Cf. A010888, A055642, A038178.

Sequence in context: A288946 A237346 A193757 * A038178 A023106 A135480

Adjacent sequences: A246602 A246603 A246604 * A246606 A246607 A246608

Keyword

base,nonn,fini,full

Author

Ivan N. Ianakiev, Aug 31 2014

Status

approved