A178501 Zero followed by powers of ten.

0, 1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 10000000000000000, 100000000000000000

Offset

0,3

Comments

The sequence S consisting of the nonnegative numbers arranged in lexicographic order according to their decimal expansion begins 0, 1, 10, 100, 1000, ..., 2, 20, 200, 2000, ..., 3, 30, ... does not have an OEIS entry, since there are uncountably many terms before 2 appears (or even before 100000010000 appears). However, S does begin with the present sequence. - N. J. A. Sloane, Dec 09 2024

a(n)^k + reverse(a(n))^k is a palindrome for any positive integer k. - Bui Quang Tuan, Mar 31 2015

Links

Table of n, a(n) for n=0..18.

Index entries for linear recurrences with constant coefficients, signature (10).

Formula

a(n+1) = A011557(n).

a(n) = A178500(n) / 10.

a(n) = (10^n - 0^n)/10. E.g.f.: exp(5*x)*sinh(5x)/5. Binomial transform of A015577. - Paul Barry, Jul 09 2003

G.f.: x/(1 - 10*x). - Chai Wah Wu, Jun 17 2020

Mathematica

Join[{0}, 10^Range[0, 19]] (* Alonso del Arte, Mar 31 2015 *)

Prog

(PARI) a(n)=10^n\10 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A131577, A140429, A178500; subsequence of A029793.

The powers of 10, A011557, is a subsequence.

Sequence in context: A136873 A135655 A178500 * A011557 A138825 A290664

Adjacent sequences: A178498 A178499 A178500 * A178502 A178503 A178504

Keyword

nonn,easy

Author

Reinhard Zumkeller, May 28 2010

Status

approved