OFFSET
1,1
COMMENTS
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.
REFERENCES
Xander Faber and Jon Grantham, "On Integers Whose Sum is the Reverse of their Product", Fib. Q., 61:1 (2023), 28-41.
LINKS
Xander Faber and Jon Grantham, On Integers Whose Sum is the Reverse of their Product, arXiv:2108.13441 [math.NT], 2021.
Index entries for linear recurrences with constant coefficients, signature (11,-10).
FORMULA
G.f.: x*(220*x^4-127*x^3-55*x^2-13*x+2)/((10*x-1)*(x-1)).
From Stefano Spezia, Mar 21 2023: (Start)
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)
EXAMPLE
2+497 = 499 and 2*497 = 994.
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
N. J. A. Sloane, Feb 27 2023
STATUS
approved