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, 1000000000000000000, 10000000000000000000, 100000000000000000000

Offset: 0

Author

Reinhard Zumkeller, May 28 2010

Keywords

• nonn
• easy

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

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

Crossrefs

Cf. A093136, A131577, A140429, A178500; subsequence of A029793.

The powers of 10, A011557, is a subsequence.

Programs

Mathematica

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

PARI

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

PARI

concat(0, Vec(-x/(10*x-1) + O(x^22))) \\ Elmo R. Oliveira, Jul 21 2025

Formula

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

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

From Paul Barry, Jul 09 2003: (Start)

a(n) = (10^n - 0^n)/10.

E.g.f.: exp(5*x)*sinh(5*x)/5.

Binomial transform of A015577. (End)

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

From Elmo R. Oliveira, Jul 21 2025: (Start)

a(n) = 10*a(n-1) for n > 1.

a(n) = A093136(n)/2 for n >= 1. (End)

Extensions

More terms from Elmo R. Oliveira, Jul 21 2025