



1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 10000000000000000, 100000000000000000, 1000000000000000000
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OFFSET

0,2


COMMENTS

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^n0^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^(n1) 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 pcolored compositions of n. For n>=1, a(n) equals the number of 10colored compositions of n such that no adjacent parts have the same color.  Milan Janjic, Nov 17 2011
Smallest n+1 digit number greater than 0 (with offset 0).  Wesley Ivan Hurt, Jan 17 2014


REFERENCES

Philip Morrison et al., Powers of Ten, Scientific American Press, 1982 and later editions.


LINKS

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).


FORMULA

a(n) = 10^n; a(n) = 10*a(n1).
G.f.: 1/(110x), e.g.f.: exp(10x)
a(n) = A159991(n)/A000400(n). [From Reinhard Zumkeller, May 02 2009]


MAPLE

A011557:=n>10^n; seq(A011557(n), n=0..40); # Wesley Ivan Hurt, Jan 17 2014


MATHEMATICA

Table[10^n, {n, 0, 40}] (*From Vladimir Joseph Stephan Orlovsky, Feb 15 2011*)


PROG

(PARI) a(n)=10^n \\ Charles R Greathouse IV, Jun 15 2011
(Haskell)
a011557 = (10 ^)
a011557_list = iterate (* 10) 1
 Reinhard Zumkeller, Jul 05 2013, Feb 05 2012
(Maxima) A011557(n):=10^n$ makelist(A011557(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */


CROSSREFS

Sequence in context: A135655 A178500 A178501 * A138825 A138824 A138823
Adjacent sequences: A011554 A011555 A011556 * A011558 A011559 A011560


KEYWORD

nonn,easy,nice


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Links to "Powers of Ten" books and videos added by N. J. A. Sloane, Nov 07 2009


STATUS

approved



