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%I #104 Sep 17 2023 11:54:27
%S 1,10,100,1000,10000,100000,1000000,10000000,100000000,1000000000,
%T 10000000000,100000000000,1000000000000,10000000000000,
%U 100000000000000,1000000000000000,10000000000000000,100000000000000000,1000000000000000000
%N Powers of 10: a(n) = 10^n.
%C Same as Pisot sequences E(1, 10), L(1, 10), P(1, 10), T(1, 10). Essentially same as Pisot sequences E(10, 100), L(10, 100), P(10, 100), T(10, 100). See A008776 for definitions of Pisot sequences.
%C Same as k^n in base k. - _Dominick Cancilla_, Aug 02 2010 [Corrected by _Jianing Song_, Sep 17 2022]
%C 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
%C Smallest n+1 digit number greater than 0 (with offset 0). - _Wesley Ivan Hurt_, Jan 17 2014
%C Numbers with digit sum = 1, or, A007953(a(n)) = 1. - _Reinhard Zumkeller_, Jul 17 2014
%C Does not satisfy Benford's law. - _N. J. A. Sloane_, Feb 14 2017
%D Philip Morrison et al., Powers of Ten, Scientific American Press, 1982 and later editions.
%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H T. D. Noe, <a href="/A011557/b011557.txt">Table of n, a(n) for n = 0..100</a>
%H Kees Boeke, <a href="http://www.vendian.org/mncharity/cosmicview/">Cosmic View: The Universe in 40 Jumps (1957)</a> [The original "powers of ten" book]
%H P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/groups.html">Sequences realized by oligomorphic permutation groups</a>, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
%H Charles and Ray Eames, <a href="http://www.youtube.com/watch?v=1Z53wTtGGA0">Powers of Ten</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H Robert Price, <a href="/A011557/a011557.txt">Comments on A011557 concerning Elementary Cellular Automata</a>, Feb 21 2016
%H Y. Puri and T. Ward, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/WARD/short.html">Arithmetic and growth of periodic orbits</a>, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
%H Science, Optics and You, <a href="http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/">Secret Worlds: The Universe Within</a> [Powers of Ten]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/10.html">10</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Digitaddition.html">Digitaddition</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Powers_of_Ten">Powers of Ten</a>
%H S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (10).
%H <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H <a href="/index/Be#Benford">Index entries for sequences related to Benford's law</a>
%F a(n) = 10^n.
%F a(n) = 10*a(n-1).
%F G.f.: 1/(1-10*x).
%F E.g.f.: exp(10*x).
%F A000005(a(n)) = A000290(n+1). - _Reinhard Zumkeller_, Mar 04 2007
%F a(n) = 60^n/6^n = A159991(n)/A000400(n). - _Reinhard Zumkeller_, May 02 2009
%F a(n) = A178501(n+1); for n > 0: a(n) = A178500(n). - _Reinhard Zumkeller_, May 28 2010
%p A011557:=n->10^n; seq(A011557(n), n=0..40); # _Wesley Ivan Hurt_, Jan 17 2014
%t Table[10^n,{n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 15 2011 *)
%t 10^Range[0,20] (* _Harvey P. Dale_, Sep 17 2023 *)
%o (PARI) a(n)=10^n \\ _Charles R Greathouse IV_, Jun 15 2011
%o (Haskell)
%o a011557 = (10 ^)
%o a011557_list = iterate (* 10) 1
%o -- _Reinhard Zumkeller_, Jul 05 2013, Feb 05 2012
%o (Maxima) A011557(n):=10^n$ makelist(A011557(n),n,0,30); /* _Martin Ettl_, Nov 05 2012 */
%o (Python)
%o print([10**n for n in range(19)]) # _Michael S. Branicky_, Jan 10 2021
%Y Cf. A242614.
%Y Cf. A178501: this sequence with 0 prefixed.
%Y Row 5 of A329332.
%K nonn,easy,nice
%O 0,2
%A _N. J. A. Sloane_
%E Links to "Powers of Ten" books and videos added by _N. J. A. Sloane_, Nov 07 2009
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