cp's OEIS Frontend

A322905 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.

%I A322905 #20 Feb 11 2019 13:27:30
%S A322905 0,144,441,1475244,4425741,161247384,483742161,14752475244,
%T A322905 44257425741,1612475247384,4837425742161,147524752475244,
%U A322905 442574257425741,16124752475247384,48374257425742161
%N A322905 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 A322905 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 A322905 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 A322905 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 A322905 For instance, 147*3=441 and 147-3=144 are terms; 161247387*3=483742161 and 161247387-3=161247384 are terms too.
%t A322905 Do[If[IntegerDigits[x y] == Reverse[IntegerDigits[y - x]], Print[{x, y, y - x, x y}]], {x, 0, 10}, {y, x, 100000000}]
%Y A322905 Cf. A004086, A166749 (sum and product of two integers).
%K A322905 nonn,easy,base
%O A322905 1,2
%A A322905 _Wang Pok Lo_, Dec 30 2018