A257829 The decimal representation of the average of the digits of n starts with the digits of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 45, 566, 1500, 2250, 3750, 18000, 383333, 4428571, 11250000, 788888888, 1000000000, 2000000000, 3000000000, 4000000000, 5000000000, 6000000000, 7000000000, 8000000000, 9000000000, 44545454545, 358333333333, 4461538461538

Offset: 1

Author

Eric Angelini and Giovanni Resta, May 10 2015

Keywords

• base
• nonn

Comments

The sequence is infinite since it contains all the numbers m*10^(10^k-1), for 1 <= m <= 9 and k >= 0.

Examples

			566 is a term since the mean of its digits is (5+6+6)/3 = 17/3 and the first 3 digits of 17/3 = 5.6666... are 566. - corrected by _Joseph L. Wetherell_, Mar 17 2018
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..876 (terms < 10^1000)

Crossrefs

Cf. A257830.

Programs

Mathematica

(* outputs terms with at most 100 digits *) sol[nd_] := Block[{z = Range[9 nd]/nd, x}, x = FromDigits /@ First /@ RealDigits[z, 10, nd]; x[[Select[Range@ Length@x, z[[#]] == Mean@ IntegerDigits@x[[#]] &]]]]; Union@ Flatten@Array[sol, 100]