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

Author

Debapriyay Mukhopadhyay, Sep 06 2016

Keywords

• nonn
• base
• easy

Examples

			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.
		

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).

Programs

Magma

[5*10^(n-1)-3: n in [1..25]]; // Vincenzo Librandi, Sep 09 2016

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 *)

PARI

isok(n) = digits(n+2) == Vecrev(digits(2*n)); \\ Michel Marcus, Sep 07 2016

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