A342143 Take a(n), sort its digits into ascending order, divide the larger of the two numbers by the smaller and keep only the remainder: this remainder is present in a(n) as a substring of its digits.

10, 20, 30, 40, 50, 52, 60, 70, 80, 90, 98, 100, 105, 106, 108, 110, 120, 130, 140, 150, 160, 170, 180, 186, 190, 198, 200, 205, 220, 230, 240, 250, 251, 260, 270, 274, 280, 290, 298, 300, 302, 330, 340, 350, 360, 370, 380, 390, 398, 400, 405, 410, 440, 450, 460, 470, 480, 490, 498, 500, 502, 510, 511

Offset: 1

Author

Eric Angelini and Carole Dubois, Mar 01 2021

Keywords

• base
• nonn

Comments

In sorting a number, leading zeros are erased.

This is the lexicographically earliest sequence of distinct positive terms with this property.

Examples

			a(1) = 10, which sorted is 1 (leading zeros are erased); 10/1 leaves a remainder 0, which is present in a(1);
a(2) = 20, which sorted is 2 (leading zeros are erased); 20/2 leaves a remainder 0, which is present in a(2);
...
a(6) = 52, which sorted is 25; 52/25 leaves a remainder 2, which is present in a(6); etc.
		

Crossrefs

Cf. A090053.

Programs

Mathematica

lst={};k=1;Do[While[!StringContainsQ[ToString@k,ToString@Mod[#2,#]&@@(Sort@{k,FromDigits@Sort@IntegerDigits@k})],k++];AppendTo[lst,k];k++,{n,62}];lst (* Giorgos Kalogeropoulos, May 08 2022 *)