

A011557


Powers of 10.


120



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
Numbers with digit sum = 1, or, A007953(a(n)) = 1.  Reinhard Zumkeller, Jul 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}] (* 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

Cf. A242614.
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



