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A100062 Denominator of the probability that an integer n occurs in the cumulative sums of the decimal digits of a random real number between 0 and 1.

%I A100062 #27 Feb 16 2025 08:32:55
%S A100062 9,81,729,6561,59049,531441,4782969,43046721,387420489,3486784401,
%T A100062 31381059609,282429536481,2541865828329,22876792454961,
%U A100062 205891132094649,1853020188851841,16677181699666569,150094635296999121
%N A100062 Denominator of the probability that an integer n occurs in the cumulative sums of the decimal digits of a random real number between 0 and 1.
%C A100062 Essentially the same as A001019 = powers of 9.
%C A100062 Also number of n-digit positive integers with no identical adjacent digits. Hence the numerator (with A052268 as denominator) of the probability that an n-digit positive integer has this property (e.g., 9/9, 81/90, 729/900, ..., where A100062(n)/A052268(n) reduces to A001019(n-1)/A011557(n-1)). - _Rick L. Shepherd_, Jun 08 2008
%H A100062 Stanislav Sykora, <a href="/A100062/b100062.txt">Table of n, a(n) for n = 1..666</a>; previous Table by Rick L. Shepherd went up to n=30.
%H A100062 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A100062 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EvilNumber.html">Evil Number</a>
%H A100062 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (9).
%F A100062 a(n) = 9^n. - _Max Alekseyev_, Mar 03 2007
%F A100062 From _Philippe Deléham_, Nov 23 2008: (Start)
%F A100062 a(n) = 9*a(n-1), n>1; a(1)=9.
%F A100062 G.f.: 9x/(1-9x). (End)
%F A100062 a(n) = A001019(n) for n>0. - _Wesley Ivan Hurt_, Apr 18 2016
%e A100062 1/9, 10/81, 100/729, 1000/6561, 10000/59049, ...
%p A100062 A100062:=n->9^n: seq(A100062(n), n=1..30); # _Wesley Ivan Hurt_, Apr 18 2016
%t A100062 9^Range[20] (* _Harvey P. Dale_, Dec 25 2012 *)
%o A100062 (PARI) \\ The 'old' approach, using the generating function:
%o A100062 s = Vec(Ser((1-x^9)/(x^10-10*x+9),x,666));
%o A100062 a = vector(#s,n,denominator(s[n])) \\ _Stanislav Sykora_, Apr 16 2016
%o A100062 (Magma) [9^n : n in [1..30]]; // _Wesley Ivan Hurt_, Apr 18 2016
%Y A100062 Cf. A001019, A011557 A052268, A100061, A100062, A271880, A271881.
%K A100062 nonn,base,frac
%O A100062 1,1
%A A100062 _Eric W. Weisstein_, Nov 01 2004
%E A100062 More terms from _Rick L. Shepherd_, Jun 08 2008