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A011557 Powers of 10: a(n) = 10^n. 377
1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 10000000000000000, 100000000000000000, 1000000000000000000 (list; graph; refs; listen; history; text; internal format)
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
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
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Wikipedia, Powers of Ten
FORMULA
a(n) = 10^n.
a(n) = 10*a(n-1).
G.f.: 1/(1-10*x).
E.g.f.: exp(10*x).
A000005(a(n)) = A000290(n+1). - Reinhard Zumkeller, Mar 04 2007
a(n) = 60^n/6^n = A159991(n)/A000400(n). - Reinhard Zumkeller, May 02 2009
a(n) = A178501(n+1); for n > 0: a(n) = A178500(n). - Reinhard Zumkeller, May 28 2010
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 *)
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
(Maxima) A011557(n):=10^n$ makelist(A011557(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */
(Python)
print([10**n for n in range(19)]) # Michael S. Branicky, Jan 10 2021
CROSSREFS
Cf. A242614.
Cf. A178501: this sequence with 0 prefixed.
Row 5 of A329332.
Sequence in context: A135655 A178500 A178501 * A138825 A290664 A290545
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

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Last modified April 20 05:55 EDT 2024. Contains 371799 sequences. (Running on oeis4.)