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A256162 Positive integers a(n) such that number of digits in decimal expansion of a(n)^a(n) is divisible by a(n). 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 6 04:36 EDT 2022. Contains 357261 sequences. (Running on oeis4.)