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A360518
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.
0
2, 9, 24, 47, 497, 4997, 49997, 499997, 4999997, 49999997, 499999997, 4999999997, 49999999997, 499999999997, 4999999999997, 49999999999997, 499999999999997, 4999999999999997, 49999999999999997, 499999999999999997, 4999999999999999997, 49999999999999999997
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
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
Cf. A276509.
Sequence in context: A339923 A204556 A185669 * A294872 A006002 A259969
KEYWORD
nonn,base,easy
AUTHOR
N. J. A. Sloane, Feb 27 2023
STATUS
approved