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A100062
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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.
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4
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9, 81, 729, 6561, 59049, 531441, 4782969, 43046721, 387420489, 3486784401, 31381059609, 282429536481, 2541865828329, 22876792454961, 205891132094649, 1853020188851841, 16677181699666569, 150094635296999121
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OFFSET
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1,1
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COMMENTS
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Essentially the same as A001019 = powers of 9.
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
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LINKS
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FORMULA
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a(n) = 9*a(n-1), n>1; a(1)=9.
G.f.: 9x/(1-9x). (End)
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EXAMPLE
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1/9, 10/81, 100/729, 1000/6561, 10000/59049, ...
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MAPLE
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MATHEMATICA
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PROG
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(PARI) \\ The 'old' approach, using the generating function:
s = Vec(Ser((1-x^9)/(x^10-10*x+9), x, 666));
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CROSSREFS
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KEYWORD
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nonn,base,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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