OFFSET
0,2
COMMENTS
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.
Same as k^n in base k. - Dominick Cancilla, Aug 02 2010 [Corrected by Jianing Song, Sep 17 2022]
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
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).
FORMULA
a(n) = 10^n.
a(n) = 10*a(n-1).
G.f.: 1/(1-10*x).
E.g.f.: exp(10*x).
Sum_{n>0} 1/a(n) = 1/9 = A000012. - Stefano Spezia, Apr 28 2024
MAPLE
MATHEMATICA
Table[10^n, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)
10^Range[0, 20] (* Harvey P. Dale, Sep 17 2023 *)
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
(Python)
print([10**n for n in range(19)]) # Michael S. Branicky, Jan 10 2021
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
Links to "Powers of Ten" books and videos added by N. J. A. Sloane, Nov 07 2009
STATUS
approved