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

1,1

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

Table of n, a(n) for n=1..22.

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

Cf. A276509.

Sequence in context: A339923 A204556 A185669 * A294872 A006002 A259969

Adjacent sequences: A360515 A360516 A360517 * A360519 A360520 A360521

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Feb 27 2023

Status

approved