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.

2, 9, 24, 47, 497, 4997, 49997, 499997, 4999997, 49999997, 499999997, 4999999997, 49999999997, 499999999997, 4999999999997, 49999999999997, 499999999999997, 4999999999999997, 49999999999999997, 499999999999999997, 4999999999999999997, 49999999999999999997

Offset: 1

Author

N. J. A. Sloane, Feb 27 2023

Keywords

• nonn
• base
• easy

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.

Examples

			2+497 = 499 and 2*497 = 994.
		

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).

Crossrefs

Cf. A276509.

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)