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A011557 Powers of 10. 120
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). 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). [From Reinhard Zumkeller, May 28 2010]

Same as n^(n-1) in base n [From Dominick Cancilla, Aug 02 2010]

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

REFERENCES

Philip Morrison et al., Powers of Ten, Scientific American Press, 1982 and later editions.

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

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

Wikipedia, Powers of Ten

Index to sequences with linear recurrences with constant coefficients, signature (10).

FORMULA

a(n) = 10^n; a(n) = 10*a(n-1).

G.f.: 1/(1-10x), e.g.f.: exp(10x)

a(n) = A159991(n)/A000400(n). [From 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 A138824 A138823

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

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Last modified September 23 04:28 EDT 2014. Contains 247089 sequences.