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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 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 AUTHOR Debapriyay Mukhopadhyay, Sep 06 2016 STATUS approved

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