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.
0, 144, 441, 1475244, 4425741, 161247384, 483742161, 14752475244, 44257425741, 1612475247384, 4837425742161, 147524752475244, 442574257425741, 16124752475247384, 48374257425742161
Offset: 1
Examples
For instance, 147*3=441 and 147-3=144 are terms; 161247387*3=483742161 and 161247387-3=161247384 are terms too.
Links
- W. P. Lo and Y. Paz, On finding all positive integers a,b such that b±a and ab are palindromic, arXiv:1812.08807 [math.HO] (2018).
Programs
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Mathematica
Do[If[IntegerDigits[x y] == Reverse[IntegerDigits[y - x]], Print[{x, y, y - x, x y}]], {x, 0, 10}, {y, x, 100000000}]
Formula
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.
Comments