Odd numbers can alyaws be made:
any odd number = n
n-1
(n-1)/2 is n and n (but you are missing the 1)
so the n and the n have to be n and n+1
so 2n+1 = is any odd number; when n is any odd number
multiples of 3 can always be made by 3 consecutive digits:
6 = 1+2+3
9 = 2+3+4
you can divide the multiple of 3 by 3 and take the consecutive digits +1 and -1 and add them:
9 is 9/3=3, 3-1=2 and 3+1=4 therefore 2+3+4 = 9
n = multiple of 3
n/3-1 + n/3 + n/3+1 = is any multiple of 3; when n is any multiple of 3
multiples of 4 +2 can always be made by 4 consecutive digits
6 = 4x1 +2 = 0+1+2+3
10 = 4x2 +2 = 1+2+3+4
you can subtract 2 then divide the multiple of 4 by 4 and take the consecutive digits -1, +2 and +1 and add them:
18 is 18-2=16, 16/4=4, 4-1=3, 4+1=5, 4+2=6 therefore 3+4+5+6
n = multiple of 4
(n-2)/4-1 + (n-2)/4 + (n-2)/4+1 + (n-2)/4+2 = is any multiple of 4+2; when n is any multiple of 4+2
multiples of ten can be made by five consecutive numbers because we call the first n