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1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 10000000000000000, 100000000000000000, 1000000000000000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Same as Pisot sequences E(1,10), L(1,10), P(1,10), T(1,10). See A008776 for definitions of Pisot sequences.
With a leading zero, this is (10^n-0^n)/10, with e.g.f. exp(5x)sinh(5x)/5. This is the binomial transform of A015577. - Paul Barry, Jul 09 2003
A000005(a(n)) = A000290(n+1). - Reinhard Zumkeller, Mar 04 2007
a(n) = A178501(n+1); for n>0: a(n) = A178500(n). [From Reinhard Zumkeller, May 28 2010]
Same as n^(n-1) in base n [From Dominick Cancilla, Aug 02 2010]
The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=1, a(n) equals the number of 10-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011
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REFERENCES
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Philip Morrison et al., Powers of Ten, Scientific American Press, 1982 and later editions.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
Kees Boeke, Cosmic View: The Universe in 40 Jumps (1957) [The original "powers of ten" book]
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
Charles and Ray Eames, Powers of Ten
Tanya Khovanova, Recursive Sequences
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
Science, Optics and You, Secret Worlds: The Universe Within [Powers of Ten]
Eric Weisstein's World of Mathematics, 10
Eric Weisstein's World of Mathematics, Digitaddition
Wikipedia, Powers of Ten
Index to sequences with linear recurrences with constant coefficients, signature (10).
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FORMULA
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a(n) = 10^n; a(n) = 10*a(n-1).
G.f.: 1/(1-10x), e.g.f.: exp(10x)
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MATHEMATICA
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Table[10^n, {n, 0, 40}] (*From Vladimir Joseph Stephan Orlovsky, Feb 15 2011*)
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PROG
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(PARI) a(n)=10^n \\ Charles R Greathouse IV, Jun 15 2011
(Haskell)
a011557 n = a011557_list !! n
a011557_list = iterate (* 10) 1 -- Reinhard Zumkeller, Feb 05 2012
(Maxima) A011557(n):=10^n$ makelist(A011557(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */
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CROSSREFS
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a(n) = A159991(n)/A000400(n). [From Reinhard Zumkeller, May 02 2009]
Sequence in context: A135655 A178500 A178501 * A138825 A138824 A138823
Adjacent sequences: A011554 A011555 A011556 * A011558 A011559 A011560
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Links to "Powers of Ten" books and videos added by N. J. A. Sloane, Nov 07 2009
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STATUS
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approved
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