%I #20 Feb 11 2019 13:27:30

%S 0,144,441,1475244,4425741,161247384,483742161,14752475244,

%T 44257425741,1612475247384,4837425742161,147524752475244,

%U 442574257425741,16124752475247384,48374257425742161

%N Sequence consists of all pairs of numbers x and y such that x is the reverse of y, and there exist numbers i and j such that x = i-j and y=i*j; the list of the numbers x and y is then sorted into ascending order and duplicates are removed.

%C The first term is trivial since 0-0=0*0=0. The pattern of 147 followed by blocks of 5247 followed by 5244 (and its reverse) continues indefinitely. This is also true for the pattern of 161247 followed by blocks of 5247 followed by 384 (and its reverse).

%H W. P. Lo and Y. Paz, <a href="https://arxiv.org/abs/1812.08807">On finding all positive integers a,b such that b±a and ab are palindromic</a>, arXiv:1812.08807 [math.HO] (2018).

%F For some positive integer k, if n=4k, a(n)=-3+147*10^(4n)+53*(10^(4n)-1)/101; if n=4k+1, a(n)=441*10^(4n)+159*(10^(4n)-1)/101; if n=4k+2, a(n)=384+161247*10^(4n-1)+53*(10^(4n-1)-10^3)/101; if n=4k+3, a(n)=1161+483741*10^(4n-1)+159*(10^(4n-1)-10^3)/101. Note that the n-th term corresponds to that of the sequence, so the formulas are valid for n>3.

%e For instance, 147*3=441 and 147-3=144 are terms; 161247387*3=483742161 and 161247387-3=161247384 are terms too.

%t Do[If[IntegerDigits[x y] == Reverse[IntegerDigits[y - x]], Print[{x, y, y - x, x y}]], {x, 0, 10}, {y, x, 100000000}]

%Y Cf. A004086, A166749 (sum and product of two integers).

%K nonn,easy,base

%O 1,2

%A _Wang Pok Lo_, Dec 30 2018