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

1,2

Comments

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

Links

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

Example

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

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]

Crossrefs

Cf. A257830.

Sequence in context: A281745 A302501 A183532 * A219327 A219326 A335205

Adjacent sequences: A257826 A257827 A257828 * A257830 A257831 A257832

Keyword

base,nonn

Author

Eric Angelini and Giovanni Resta, May 10 2015

Status

approved