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A088924
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Number of "9ish numbers" with n digits.
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7
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1, 18, 252, 3168, 37512, 427608, 4748472, 51736248, 555626232, 5900636088, 62105724792, 648951523128, 6740563708152, 69665073373368, 716985660360312, 7352870943242808, 75175838489185272, 766582546402667448
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OFFSET
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1,2
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COMMENTS
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First difference of A016189. ("9" can be replaced by any other nonzero digit, however only the 9ish numbers are closed under lunar multiplication.)
See A257285 - A257289 for first differences of 5^n-4^n, ..., 9^n-8^n. These also give the number of n-digit numbers whose largest digit is 5, 6, 7, 8, respectively. - M. F. Hasler, May 04 2015
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LINKS
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D. Applegate, M. LeBrun, and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
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FORMULA
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a(n) = 9*10^(n-1) - 8*9^(n-1).
G.f.: x*(1 - x)/(1 - 19*x + 90*x^2). - Bobby Milazzo, May 02 2014
E.g.f.: (81*exp(10*x) - 80*exp(9*x) - 1)/90. - Stefano Spezia, Nov 16 2023
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EXAMPLE
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a(2) = 18 because 19, 29, 39, 49, 59, 69, 79, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98 and 99 are the eighteen two-digit 9ish numbers.
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MAPLE
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MATHEMATICA
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Series[(x (1 - x))/(1 - 19 x + 90 x^2), {x, 0, 10}] (* Bobby Milazzo, May 02 2014 *)
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PROG
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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STATUS
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approved
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