Help! A remainder is chasing me ... #2

[Guest]

The following puzzle is a variation of the question posted by bonanova.

I just found a number with an interesting property:

When I divide it by 2, the remainder is 1.

When I divide it by 3, the remainder is 1.

When I divide it by 4, the remainder is 1.

When I divide it by 5, the remainder is 1.

When I divide it by 6, the remainder is 1.

When I divide it by 7, the remainder is 1.

When I divide it by 8, the remainder is 1.

When I divide it by 9, the remainder is 1.

When I divide it by 10, the remainder is 1.

But when I divide it by 11, the remainder is 0.

Can you find it?

[unreality]

Well obviously its a multiple of 11 and the number 1 beneath it is divisible by a bunch of numbers

[Guest]

I had to big time brute this one, but I got a few that work. <!-- s:mrgreen: --><!-- s:mrgreen: -->

Smallest.

25201

11*2291

10*2520+1

9*2800+1

8*3150+1

7*3600+1

6*4200+1

5,4,3 are just 10,8,6 *2

2 just has to be an odd number

Others

52921

80641

108361

136081

163801

191521

219241

I am guessing this is an infinite set

Edited to add a couple more numbers

[unreality]

I could write a computer program but it looks like ^ has already solved it