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0, 9, 99, 999, 9999, 99999, 999999, 9999999, 99999999, 999999999, 9999999999, 99999999999, 999999999999, 9999999999999, 99999999999999, 999999999999999, 9999999999999999, 99999999999999999
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A friend from Germany remarks that the sequence 9, 99, 999, 9999, 99999, 999999, ... might be called the grumpy German sequence: nein!, nein! nein!, nein! nein! nein!, ...
a(n) = A075412(n)/A002275(n) = A178630(n)/A002276(n) = A178631(n)/A002277(n) = A075415(n)/A002278(n) = A178632(n)/A002279(n) = A178633(n)/A002280(n) = A178634(n)/A002281(n) = A178635(n)/A002282(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 31 2010]
For n>0: A007953(a(n))=A008591(n) and A010888(a(n))=9. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 06 2010]
The Regan link shows that integers of the form 10^n -1 have binary representations with exactly n trailing 1 bits. Also those integers have quinary expressions with exactly n trailing digits 4. For example, 10^4 -1 = (304444)5. The first digits in quinary correspond to the number 2^n -1, in our example (30)5 = 2^4 -1. A similar pattern occurs in the binary case. Consider 9 = (1001)2. [From W. Bomfim (webonfim(AT)bol.com) Dec 23 2010]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..100
Index entries for sequences related to linear recurrences with constant coefficients
Rick Regan, Nines in quinary
Index to sequences with linear recurrences with constant coefficients, signature (11,-10).
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FORMULA
| G.f.: 1/(1-10*x)-1/(1-x). E.g.f.: e^(10*x)-e^x. [From Mohammad K. Azarian (azarian(AT)evansville.edu), Jan 14 2009]
a(n)=10*a(n-1)+9, with a(0)=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Jan 23 2009]
a(n)=a(n-1)+9*10^(n-1) with a(0)=0; Also: a(n)=11*a(n-1)-10*a(n-2) with a(0)=0, a(1)=9. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jul 22 2010]
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PROG
| (MAGMA) [(10^n-1): n in [0..20]]; // Vincenzo Librandi, Apr 26 2011
(PARI) a(n)=10^n-1 \\ Charles R Greathouse IV, Jan 30 2012
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CROSSREFS
| Cf. A007138, A003020.
Sequence in context: A070843 A108908 A116260 * A103456 A155157 A015685
Adjacent sequences: A002280 A002281 A002282 * A002284 A002285 A002286
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KEYWORD
| easy,nonn,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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