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Search: id:A052386
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| A052386 |
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Number of integers from 1 to 10^n-1 that lack 0 as a digit. |
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+0
9
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| 0, 9, 90, 819, 7380, 66429, 597870, 5380839, 48427560, 435848049, 3922632450, 35303692059, 317733228540, 2859599056869, 25736391511830, 231627523606479, 2084647712458320, 18761829412124889, 168856464709124010
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OFFSET
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0,2
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FORMULA
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a(n) = 9*a(n-1) + 9.
a(n) = 9(9^n-1)/8 = sum_{j=1..n} 9^j = a(n-1)+9^n = 9*A002452(n) = A002452(n+1)-1; write A000918(n+1) in base 2 and read as if written in base 9. - Henry Bottomley (se16(AT)btinternet.com), Aug 30 2001
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EXAMPLE
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For n=2, the numbers from 1 to 99 which *have* 0 as a digit are the 9 numbers 10, 20, 30, ..., 90. So a(1) = 99 - 9 = 90.
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MAPLE
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a:=n->sum (9^j, j=1..n): seq(a(n), n=0..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 03 2007
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MATHEMATICA
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Table[9(9^n - 1)/8, {n, 0, 20}]
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CROSSREFS
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Cf. A024101, A052379.
Sequence in context: A044641 A165135 A054616 this_sequence A158609 A057092 A156577
Adjacent sequences: A052383 A052384 A052385 this_sequence A052387 A052388 A052389
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KEYWORD
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easy,nonn,base
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AUTHOR
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Odimar Fabeny (fabeny(AT)braznet.com.br), Mar 10 2000
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EXTENSIONS
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More terms and revised description from James A. Sellers (sellersj(AT)math.psu.edu), Mar 13 2000 and from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 14 2003
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