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A053541
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a(n)=n*10^(n-1).
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9
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1, 20, 300, 4000, 50000, 600000, 7000000, 80000000, 900000000, 10000000000, 110000000000, 1200000000000, 13000000000000, 140000000000000, 1500000000000000, 16000000000000000, 170000000000000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This sequence gives the number of 1's (or any other digit) required to write all integers of n or fewer digits. It is thus A094798 for n=9, 99, 999, .... Another formula: a(n) = 10*a(n-1)+10(n-1) a(n) = Sum_{k=1...n} k*C(n,k)*9^(n-k) - Jason D. W. Taff (jtaff(AT)jburroughs.org), Dec 05 2004
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..100
F. Ellermann, Illustration of binomial transforms
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FORMULA
| a(n)=20*a(n-1)-100*a(n-2); a(0)=1; n>0.
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MATHEMATICA
| f[n_]:=n*10^(n-1); f[Range[40]] (*From Vladimir Joseph Stephan Orlovsky, Feb 09 2011*)
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PROG
| (MAGMA) [n*10^(n-1): n in [1..30]]; // Vincenzo Librandi, Jun 06 2011
(PARI) a(n)=n*10^(n-1) \\ Charles R Greathouse IV, Dec 05 2011
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CROSSREFS
| Cf. A001787, A053464, A053469, A094798, A038303.
Sequence in context: A138794 A077758 A202270 * A004345 A001755 A016190
Adjacent sequences: A053538 A053539 A053540 * A053542 A053543 A053544
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, Jan 15 2000
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), May 29 2001
Offset changed from 0 to 1 by Vincenzo Librandi, Jun 06 2011
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