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A276509 Numbers k in base 10 such that the digits of 2 + k are the digits of 2k written in reverse order. 1
2, 47, 497, 4997, 49997, 499997, 4999997, 49999997, 499999997, 4999999997, 49999999997, 499999999997, 4999999999997, 49999999999997, 499999999999997, 4999999999999997, 49999999999999997, 499999999999999997, 4999999999999999997, 49999999999999999997, 499999999999999999997 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Xander Faber and Jon Grantham, On Integers Whose Sum is the Reverse of their Product, arXiv:2108.13441 [math.NT], 2021.
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
KEYWORD
nonn,base
AUTHOR
STATUS
approved

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Last modified July 23 19:18 EDT 2024. Contains 374553 sequences. (Running on oeis4.)