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A199682
a(n) = 2*10^n + 1.
10
3, 21, 201, 2001, 20001, 200001, 2000001, 20000001, 200000001, 2000000001, 20000000001, 200000000001, 2000000000001, 20000000000001, 200000000000001, 2000000000000001, 20000000000000001, 200000000000000001, 2000000000000000001
OFFSET
0,1
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
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
MATHEMATICA
NestList[10#-9&, 3, 20] (* or *) LinearRecurrence[{11, -10}, {3, 21}, 20] (* Harvey P. Dale, Sep 30 2017 *)
PROG
(Magma) [2*10^n+1: n in [0..30]];
(Haskell)
a199682 = (+ 1) . (* 2) . (10 ^) -- Reinhard Zumkeller, Jan 30 2015
(PARI) a(n)=2*10^n+1 \\ Charles R Greathouse IV, Oct 16 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Nov 09 2011
STATUS
approved