A169830 Numbers k such that 2*reverse(k) - k = 1.
1, 73, 793, 7993, 79993, 799993, 7999993, 79999993, 799999993, 7999999993, 79999999993, 799999999993, 7999999999993, 79999999999993, 799999999999993, 7999999999999993, 79999999999999993, 799999999999999993, 7999999999999999993, 79999999999999999993, 799999999999999999993
Offset: 1
Links
- Matthew House, Table of n, a(n) for n = 1..996
- Erich Friedman, What's Special About This Number? (See entry 73)
- David Radcliffe, Numbers that are nearly doubled when reversed.
- Index entries for linear recurrences with constant coefficients, signature (11,-10).
Programs
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Mathematica
k = 1; lst = {}; fQ[n_] := 2 FromDigits@ Reverse@ IntegerDigits@n == 1 + n; While[k < 10^8, If[fQ@k, Print@k; AppendTo[lst, k]]; k++ ]; lst (* Robert G. Wilson v, Jun 01 2010 *) Rest@ CoefficientList[Series[x (1 + 62 x)/((1 - x) (1 - 10 x)), {x, 0, 20}], x] (* or *) Table[If[n == 1, 1, FromDigits@ Join[{7}, ConstantArray[9, n - 2], {3}]], {n, 20}] (* or *) LinearRecurrence[{11, -10}, {1, 73}, 20] (* Michael De Vlieger, Feb 12 2017 *) -
PARI
isok(n) = 2*fromdigits(Vecrev(digits(n))) - n == 1; \\ Michel Marcus, Feb 12 2017
Formula
a(n) = 8*10^(n-1) - 7. - David Radcliffe, Jul 25 2015
From Matthew House, Feb 12 2017: (Start)
G.f.: x*(1+62*x)/((1-x)*(1-10*x)).
a(n) = 11*a(n-1) - 10*a(n-2). (End)
E.g.f.: (31 - 35*exp(x) + 4*exp(10*x))/5. - Elmo R. Oliveira, Jun 12 2025
Extensions
a(6)-a(8) from Robert G. Wilson v, Jun 01 2010
More terms from David Radcliffe, Jul 25 2015
Comments