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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
0, 144, 441, 1475244, 4425741, 161247384, 483742161, 14752475244, 44257425741, 1612475247384, 4837425742161, 147524752475244, 442574257425741, 16124752475247384, 48374257425742161
OFFSET
1,2
COMMENTS
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).
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.
EXAMPLE
For instance, 147*3=441 and 147-3=144 are terms; 161247387*3=483742161 and 161247387-3=161247384 are terms too.
MATHEMATICA
Do[If[IntegerDigits[x y] == Reverse[IntegerDigits[y - x]], Print[{x, y, y - x, x y}]], {x, 0, 10}, {y, x, 100000000}]
CROSSREFS
Cf. A004086, A166749 (sum and product of two integers).
Sequence in context: A188246 A258382 A151820 * A281240 A014770 A131528
KEYWORD
nonn,easy,base
AUTHOR
Wang Pok Lo, Dec 30 2018
STATUS
approved