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Search: id:A011557
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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; listen)
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OFFSET
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0,2
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COMMENT
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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 (pbarry(AT)wit.ie), Jul 09 2003
A000005(a(n)) = A000290(n+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 04 2007
With a different offset, number of n-permutations (n>=0) of 11 objects: p, q, r, s, t, u, v, w, z, x, y with repetition allowed, containing exactly zero (0) or free u's. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 15 2008
a(n) = sequence A000079(n) written in base 2: (n+1)times 1 and n times 0. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Aug 02 2009]
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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, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Wikipedia, Powers of Ten
Index entries for sequences related to linear recurrences with constant coefficients
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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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MAPLE
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with(finance):seq(futurevalue(1, 9, n), n=0..18); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2009]
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CROSSREFS
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a(n) = A159991(n)/A000400(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 02 2009]
Sequence in context: A086067 A136873 A135655 this_sequence A138825 A138824 A138823
Adjacent sequences: A011554 A011555 A011556 this_sequence 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 (njas(AT)research.att.com).
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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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