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A360518
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Numbers j such that there exists a number i <= j with the property that i+j and i*j have the same decimal digits in reverse order.
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0
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2, 9, 24, 47, 497, 4997, 49997, 499997, 4999997, 49999997, 499999997, 4999999997, 49999999997, 499999999997, 4999999999997, 49999999999997, 499999999999997, 4999999999999997, 49999999999999997, 499999999999999997, 4999999999999999997, 49999999999999999997
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OFFSET
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1,1
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COMMENTS
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The pairs (i,j) are (2,2), (9,9), (3,24), (2,47), (2,497), (2,4997), (2,49997), (2,499997), (2,4999997), (2,49999997), ...
These pairs, together with all pairs (2,4999..997), comprise the complete list.
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REFERENCES
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Xander Faber and Jon Grantham, "On Integers Whose Sum is the Reverse of their Product", Fib. Q., 61:1 (2023), 28-41.
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LINKS
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FORMULA
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G.f.: x*(220*x^4-127*x^3-55*x^2-13*x+2)/((10*x-1)*(x-1)).
a(n) = (10^n - 600)/200 for n > 3.
E.g.f.: (1797 - 1800*exp(x) + 3*exp(10*x) + 2970*x + 3450*x^2 + 2200*x^3)/600. (End)
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EXAMPLE
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2+497 = 499 and 2*497 = 994.
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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