A320522 Numbers k such that k^10 divides 10^k.

1, 10, 20, 25, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 625, 640, 800, 1000, 1024, 1250, 1280, 1600, 2000, 2048, 2500, 2560, 3125, 3200, 4000, 4096, 5000, 5120, 6250, 6400, 8000, 8192, 10000, 10240, 12500, 12800, 15625, 16000

Offset

1,2

Comments

The sequence consists of the numbers of the form 2^i*5^j (A003592) except for {2, 4, 5, 8, 16, 32}. - Giovanni Resta, Nov 13 2018

Links

Table of n, a(n) for n=1..47.

Example

20 is in the sequence because 20^10 divides 10^20.
5 is not in the sequence because 5^10 does not divide 10^5.

Mathematica

Select[Union@ Flatten@ Table[2^a * 5^b, {a, 0, Log[2, #/(1)]}, {b, 0, Log[5, #/(2^a)]}] &[10^5], PowerMod[10, #, #^10] == 0 &] (* Michael De Vlieger, Oct 15 2018 *)
m = 10^5; DeleteCases[Union @@ Table[2^a*5^b, {a, 0, Log2@ m}, {b, Boole[0 < a < 6], Log[5, m/2^a]}], 5] (* Giovanni Resta, Nov 13 2018 *)

Prog

(PARI) isok(n) = Mod(10, n^10)^n == 0; \\ Michel Marcus, Oct 14 2018
(GAP) Filtered([1..16000], k->PowerMod(10, k, k^10)=0); # Muniru A Asiru, Oct 16 2018

Crossrefs

Subsequence of A003592 (numbers of the form 2^i*5^j).

Cf. A008454 (n^10), A011557 (10^n),

Sequence in context: A199978 A342142 A179819 * A072592 A229305 A229304

Adjacent sequences: A320519 A320520 A320521 * A320523 A320524 A320525

Keyword

nonn

Author

Kritsada Moomuang, Oct 14 2018

Status

approved