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A246605 Numbers n such that n = (digital root of n)^(number of digits of n). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 29 16:38 EDT 2020. Contains 333107 sequences. (Running on oeis4.)