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%I #51 Sep 22 2023 12:16:15
%S 0,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,
%T 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,
%U 9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9
%N Zero followed by infinitely many 9's.
%C Another interpretation: A real number with an infinitesimally small difference from the integer 1 which is used to test the precision of calculating devices. - _John W. Nicholson_, Feb 01 2012
%C a(n) is also the number of n-digit positive repdigit numbers (A010785). - _Stefano Spezia_, Aug 15 2020
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F a(0) = 0, a(n) = 9 for n > 0.
%F a(n) = 9 * A057427(n).
%F a(n) = A010888(9*n), where A010888 is the digital root.
%F From _Robert Israel_, Dec 16 2014: (Start)
%F G.f.: 9*x/(1 - x).
%F E.g.f.: 9*(exp(x) - 1). (End)
%e Viewed as a real number: For a TI-89, entering 1.-10^-12 yields .999999999999; however, 1.-10^-13 yields 1. - _John W. Nicholson_, Feb 01 2012
%t a[n_] := Mod[9 n - 1, 9] + 1; a[0] = 0; Array[a, 105, 0] (* _Robert G. Wilson v_, Sep 20 2010 *)
%t PadRight[{0},120,9] (* _Harvey P. Dale_, May 03 2019 *)
%o (PARI) a(n)=if(n,9,0) \\ _Charles R Greathouse IV_, Jan 04 2013
%Y Cf. A007953, A010785, A010888, A057427, A180592, A180594, A180595, A180596, A180597, A180598.
%K easy,nonn
%O 0,2
%A _Odimar Fabeny_, Sep 10 2010
%E More terms from _Robert G. Wilson v_, Sep 20 2010
%E Definition changed by _N. J. A. Sloane_, Feb 04 2012
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