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%I #18 Mar 22 2023 08:06:33
%S 2,9,24,47,497,4997,49997,499997,4999997,49999997,499999997,
%T 4999999997,49999999997,499999999997,4999999999997,49999999999997,
%U 499999999999997,4999999999999997,49999999999999997,499999999999999997,4999999999999999997,49999999999999999997
%N 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.
%C 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), ...
%C These pairs, together with all pairs (2,4999..997), comprise the complete list.
%D Xander Faber and Jon Grantham, "On Integers Whose Sum is the Reverse of their Product", Fib. Q., 61:1 (2023), 28-41.
%H Xander Faber and Jon Grantham, <a href="https://arxiv.org/abs/2108.13441">On Integers Whose Sum is the Reverse of their Product</a>, arXiv:2108.13441 [math.NT], 2021.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-10).
%F G.f.: x*(220*x^4-127*x^3-55*x^2-13*x+2)/((10*x-1)*(x-1)).
%F From _Stefano Spezia_, Mar 21 2023: (Start)
%F a(n) = (10^n - 600)/200 for n > 3.
%F E.g.f.: (1797 - 1800*exp(x) + 3*exp(10*x) + 2970*x + 3450*x^2 + 2200*x^3)/600. (End)
%e 2+497 = 499 and 2*497 = 994.
%Y Cf. A276509.
%K nonn,base,easy
%O 1,1
%A _N. J. A. Sloane_, Feb 27 2023
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