A169830 Numbers n such that 2*reverse(n) - n = 1.

1, 73, 793, 7993, 79993, 799993, 7999993, 79999993, 799999993, 7999999993, 79999999993, 799999999993, 7999999999993, 79999999999993, 799999999999993, 7999999999999993, 79999999999999993, 799999999999999993, 7999999999999999993, 79999999999999999993

Offset

1,2

Comments

The sequence is infinite since it contains all numbers of the form 799...9993. (Cf. A101155, A101849.) [Ulrich Krug (leuchtfeuer37(AT)gmx.de), Jun 02 2010]

All numbers of the form 8*10^k-7 are members, but are there any others? - Robert G. Wilson v, Jun 01 2010

All solutions are of the form 8*10^k-7. - David Radcliffe, Jul 25 2015

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).

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)

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 *)

Prog

(PARI) isok(n) = 2*fromdigits(Vecrev(digits(n))) - n == 1; \\ Michel Marcus, Feb 12 2017

Crossrefs

Same sequence as A100412. Digit reversals of A083818.

Sequence in context: A066101 A272768 A100412 * A197341 A104907 A296024

Adjacent sequences: A169827 A169828 A169829 * A169831 A169832 A169833

Keyword

nonn,base

Author

N. J. A. Sloane, May 31 2010

Extensions

a(6)-a(8) from Robert G. Wilson v, Jun 01 2010

More terms from David Radcliffe, Jul 25 2015

Status

approved