The number of pairs of consecutive integers in the set $s=\{1000,1001,1002,\mathrm{....2000}\}$ So that no carrying is required when the two integers are added is equal to 

Let n have a decimal representation 1abc. If one of a, b or c is 5,6,7 or 8 then there will be carrying when n and n+1 are added. If n is not one of the integers described above then n has one of the forms 1abc,1ab9,1a99,1999 where $a,b,c\in \{0,1,2,3,4\}$ for such n .no carrying is required when n and n+1 are added Hence there are $5^3+5^2+5+1=156$ (such values of n)