A256162 Positive integers a(n) such that number of digits in decimal expansion of a(n)^a(n) is divisible by a(n).

1, 8, 9, 98, 99, 998, 999, 9998, 9999, 99998, 99999, 999998, 999999, 9999998, 9999999, 99999998, 99999999, 999999998, 999999999, 9999999998, 9999999999, 99999999998, 99999999999, 999999999998, 999999999999, 9999999999998, 9999999999999

Offset

1,2

Comments

A055642(a(n)^a(n)) = A055642(a(n))*a(n).

1 + floor(log_10(a(n)^a(n))) = a(n)*(1 + floor(log_10(a(n)))).

Links

Bui Quang Tuan, Table of n, a(n) for n = 1..101

Formula

a(n) = 10^floor(n/2) - 2*floor(n/2) + n - 2 = 10^floor(n/2)-(1+(-1)^n)/2 - 1 for n>1, a(1) = 1.

Example

1^1 = 1 has 1 digit, and 1 is divisible by 1.
8^8 = 16777216 has 8 digits, and 8 is divisible by 8.
98^98 has 196 digits, and 196 is divisible by 98.

Mathematica

Select[Range@10000, Mod[IntegerLength[#^#], #] == 0 &] (* Michael De Vlieger, Mar 17 2015 *)
Join[{1}, Table[(10^Floor[n/2] - 2 Floor[n/2] + n - 2), {n, 2, 30}]] (* Vincenzo Librandi, Mar 18 2015 *)

Prog

(PARI) isok(n) = !(#digits(n^n) % n); \\ Michel Marcus, Mar 17 2015
(Magma) [1] cat [10^Floor((n+1)/2)-2*Floor((n+1)/2)+n-1: n in [1..30]]; // Vincenzo Librandi, Mar 18 2015

Crossrefs

Cf. A055642 (Number of digits in decimal expansion of n).

Sequence in context: A248290 A256341 A116249 * A175556 A165467 A239584

Adjacent sequences: A256159 A256160 A256161 * A256163 A256164 A256165

Keyword

nonn,base

Author

Bui Quang Tuan, Mar 17 2015

Status

approved