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A011557 Powers of 10: a(n) = 10^n.

%I A011557 #113 Feb 16 2025 08:32:32
%S A011557 1,10,100,1000,10000,100000,1000000,10000000,100000000,1000000000,
%T A011557 10000000000,100000000000,1000000000000,10000000000000,
%U A011557 100000000000000,1000000000000000,10000000000000000,100000000000000000,1000000000000000000
%N A011557 Powers of 10: a(n) = 10^n.
%C A011557 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 A011557 Same as k^n in base k. - _Dominick Cancilla_, Aug 02 2010 [Corrected by _Jianing Song_, Sep 17 2022]
%C A011557 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 A011557 Smallest n+1 digit number greater than 0 (with offset 0). - _Wesley Ivan Hurt_, Jan 17 2014
%C A011557 Numbers with digit sum = 1, or, A007953(a(n)) = 1. - _Reinhard Zumkeller_, Jul 17 2014
%C A011557 Does not satisfy Benford's law. - _N. J. A. Sloane_, Feb 14 2017
%D A011557 Philip Morrison et al., Powers of Ten, Scientific American Press, 1982 and later editions.
%D A011557 S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
%H A011557 T. D. Noe, <a href="/A011557/b011557.txt">Table of n, a(n) for n = 0..100</a>
%H A011557 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 A011557 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 A011557 Charles and Ray Eames, <a href="http://www.youtube.com/watch?v=1Z53wTtGGA0">Powers of Ten</a>
%H A011557 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A011557 Robert Price, <a href="/A011557/a011557.txt">Comments on A011557 concerning Elementary Cellular Automata</a>, Feb 21 2016
%H A011557 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 A011557 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 A011557 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/10.html">10</a>
%H A011557 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Digitaddition.html">Digitaddition</a>
%H A011557 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A011557 Wikipedia, <a href="http://en.wikipedia.org/wiki/Powers_of_Ten">Powers of Ten</a>
%H A011557 S. Wolfram, <a href="http://wolframscience.com/">A New Kind of Science</a>
%H A011557 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (10).
%H A011557 <a href="https://oeis.org/wiki/Index_to_Elementary_Cellular_Automata">Index to Elementary Cellular Automata</a>
%H A011557 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%H A011557 <a href="/index/Be#Benford">Index entries for sequences related to Benford's law</a>
%F A011557 a(n) = 10^n.
%F A011557 a(n) = 10*a(n-1).
%F A011557 G.f.: 1/(1-10*x).
%F A011557 E.g.f.: exp(10*x).
%F A011557 A000005(a(n)) = A000290(n+1). - _Reinhard Zumkeller_, Mar 04 2007
%F A011557 a(n) = 60^n/6^n = A159991(n)/A000400(n). - _Reinhard Zumkeller_, May 02 2009
%F A011557 a(n) = A178501(n+1); for n > 0: a(n) = A178500(n). - _Reinhard Zumkeller_, May 28 2010
%F A011557 Sum_{n>0} 1/a(n) = 1/9 = A000012. - _Stefano Spezia_, Apr 28 2024
%p A011557 A011557:=n->10^n; seq(A011557(n), n=0..40); # _Wesley Ivan Hurt_, Jan 17 2014
%t A011557 Table[10^n,{n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 15 2011 *)
%t A011557 10^Range[0,20] (* _Harvey P. Dale_, Sep 17 2023 *)
%o A011557 (PARI) a(n)=10^n \\ _Charles R Greathouse IV_, Jun 15 2011
%o A011557 (Haskell)
%o A011557 a011557 = (10 ^)
%o A011557 a011557_list = iterate (* 10) 1
%o A011557 -- _Reinhard Zumkeller_, Jul 05 2013, Feb 05 2012
%o A011557 (Maxima) A011557(n):=10^n$ makelist(A011557(n),n,0,30); /* _Martin Ettl_, Nov 05 2012 */
%o A011557 (Python)
%o A011557 print([10**n for n in range(19)]) # _Michael S. Branicky_, Jan 10 2021
%Y A011557 Cf. A000005, A000012, A000290, A000400, A007953, A008776, A159991, A178500, A242614.
%Y A011557 Cf. A178501: this sequence with 0 prefixed.
%Y A011557 Row 5 of A329332.
%K A011557 nonn,easy,nice
%O A011557 0,2
%A A011557 _N. J. A. Sloane_
%E A011557 Links to "Powers of Ten" books and videos added by _N. J. A. Sloane_, Nov 07 2009