A276509 Numbers k in base 10 such that the digits of 2 + k are the digits of 2k written in reverse order.

2, 47, 497, 4997, 49997, 499997, 4999997, 49999997, 499999997, 4999999997, 49999999997, 499999999997, 4999999999997, 49999999999997, 499999999999997, 4999999999999997, 49999999999999997, 499999999999999997, 4999999999999999997, 49999999999999999997, 499999999999999999997

Offset

1,1

Links

Table of n, a(n) for n=1..21.

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

a(n) = 5 * 10^(n - 1) - 3. - Peter Bala, Sep 06 2016

G.f.: x*(2 + 25*x)/(1 - 11*x + 10*x^2). - Michael De Vlieger, Sep 06 2016

E.g.f.: (exp(10*x) - 6*exp(x) + 5)/2. - Stefano Spezia, Mar 04 2023

Example

47 is in the sequence because 47 + 2 = 49 and 47*2 = 94.
497 is in the sequence because 497 + 2 = 499 and 497*2 = 994.

Mathematica

Select[Range[10^6], IntegerDigits[# + 2] == Reverse@ IntegerDigits[2 #] &] (* or *)
Table[5 (10^(n - 1)) - 3, {n, 22}] (* or *)
CoefficientList[Series[x(2 + 25 x)/(1 - 11 x + 10 x^2), {x, 0, 21}], x] (* or *)
{2}~Join~Table[FromDigits@ Join[{4}, ConstantArray[9, {n - 2}], {7}], {n, 2, 22}] (* Michael De Vlieger, Sep 06 2016 *)

Prog

(PARI) isok(n) = digits(n+2) == Vecrev(digits(2*n)); \\ Michel Marcus, Sep 07 2016
(Magma) [5*10^(n-1)-3: n in [1..25]]; // Vincenzo Librandi, Sep 09 2016

Crossrefs

Sequence in context: A128822 A226420 A160922 * A120050 A112783 A277655

Adjacent sequences: A276506 A276507 A276508 * A276510 A276511 A276512

Keyword

nonn,base,easy

Author

Debapriyay Mukhopadhyay, Sep 06 2016

Status

approved