A065447 Concatenation of 1, 00, 111, 0000, ..., n 1's (if n is odd) or n 0's (if n is even).

1, 100, 100111, 1001110000, 100111000011111, 100111000011111000000, 1001110000111110000001111111, 100111000011111000000111111100000000, 100111000011111000000111111100000000111111111, 1001110000111110000001111111000000001111111110000000000

Offset: 1

Author

Lior Manor, Nov 18 2001

Keywords

• base
• easy
• nonn

Comments

a(n) is divisible by A002275([(n+1)/2]) = (10^[(n+1)/2]-1)/9. Cf. A262806. - Max Alekseyev, Jun 02 2013

The unique sequence of binary words a(n) such that the k-th run of a(n) has length k, for k = 1..n . - Clark Kimberling, Mar 08 2024

Examples

			a(2) = 100, the concatenation of one 1, two 0's.
a(3) = 100111, the concatenation of one 1, two 0's, three 1's.
a(4) = 1001110000, the concatenation of one 1, two 0's, three 1's, four 0's.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..44

Crossrefs

For decimal version see A065760.

Cf. A000217, A065761, A371032.

Programs

Maple

a:= n-> parse(cat((irem(i,2)$i)$i=1..n)):
seq(a(n), n=1..10);  # Alois P. Heinz, Mar 08 2024

Mathematica

FoldList[Join, {1}, Map[ConstantArray[Mod[#, 2], #] &, Range[2, 10]]] (* Peter J. C. Moses, Mar 08 2024 *)

PARI

{ m=10; for (n=1, 44, if (n==1, a=1, m*=10; a*=m; if (n%2, a+=(m - 1)/9)); write("b065447.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 19 2009