A199682 a(n) = 2*10^n + 1.

3, 21, 201, 2001, 20001, 200001, 2000001, 20000001, 200000001, 2000000001, 20000000001, 200000000001, 2000000000001, 20000000000001, 200000000000001, 2000000000000001, 20000000000000001, 200000000000000001, 2000000000000000001

Offset: 0

Author

Vincenzo Librandi, Nov 09 2011

Keywords

• nonn
• easy

Comments

Numbers k such that (R(k) - 1)/(k + 1) = 1/2, where R(k) denotes the digit reversal of k (cf. A004086). - Stefano Spezia, Nov 25 2023

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A004086, A011557, A133384.

Programs

Haskell

a199682 = (+ 1) . (* 2) . (10 ^)  -- Reinhard Zumkeller, Jan 30 2015

Magma

[2*10^n+1: n in [0..30]];

Mathematica

NestList[10#-9&,3,20] (* or *) LinearRecurrence[{11,-10},{3,21},20] (* Harvey P. Dale, Sep 30 2017 *)

PARI

a(n)=2*10^n+1 \\ Charles R Greathouse IV, Oct 16 2015

Formula

a(n) = 10*a(n-1)-9.

a(n) = 11*a(n-1)-10*a(n-2).

G.f.: 3*(1-4*x)/((1-x)*(1-10*x)).

E.g.f.: 2*exp(10*x) + exp(x). - Stefano Spezia, Nov 25 2023