

A011557


Powers of 10: a(n) = 10^n.


181



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^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).  Reinhard Zumkeller, May 28 2010
Same as n^(n1) in base n.  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
Does not satisfy Benford's law.  N. J. A. Sloane, Feb 14 2017


REFERENCES

Philip Morrison et al., Powers of Ten, Scientific American Press, 1982 and later editions.
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.


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
Robert Price, Comments on A011557 concerning Elementary Cellular Automata, Feb 21 2016
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
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Wikipedia, Powers of Ten
S. Wolfram, A New Kind of Science
Index entries for linear recurrences with constant coefficients, signature (10).
Index to Elementary Cellular Automata
Index entries for sequences related to cellular automata
Index entries for sequences related to Benford's law


FORMULA

a(n) = 10^n.
a(n) = 10*a(n1).
G.f.: 1/(110*x).
E.g.f.: exp(10*x).
a(n) = A159991(n)/A000400(n).  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 A290664 A290545
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



