A266926 a(0)=0, a(1)=1, a(2)=10; for n>2, a(n) = concat(a(1), ..., a(n-1)).

0, 1, 10, 110, 110110, 110110110110, 110110110110110110110110, 110110110110110110110110110110110110110110110110, 110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110110

Offset: 0

Author

Giovanni Teofilatto, Jan 06 2016

Keywords

• nonn
• base
• easy

Comments

Decimal conversions: 0, 1, 2, 6, 54, 3510, 14380470, 241264265751990, 67909853583655146508751957430, ... . (See A267348.) - Michael De Vlieger, Jan 06 2016

After 10, a(n) is '110' repeated 2^(n-3) times. Therefore, for n>3, a(n) is the concatenation of a(n-1) with itself.

After 1, each term with the 0's omitted is a member of A136308.

The number of digits in a(n) is A098011(n+1).

The number of digits in a(n+2)/a(n+1) gives A103204 with 2 repeated.

Examples

			a(3) = concat(1, 10, 110) = 110110.
a(4) = concat(1, 10, 110, 110110) = 110110110110.
		

Crossrefs

Cf. A000079, A098011, A103204, A136308, A267348.

Programs

Magma

[n le 2 select n*5^(n-1) else 110*(10^(3*2^(n-3))-1)/999: n in [0..8]]; // Bruno Berselli, Jan 29 2016

Mathematica

a = {0, 1}; Do[AppendTo[a, FromDigits@ Flatten@ Map[IntegerDigits@ # &, If[n < 2, Reverse@ a, a]]], {n, 8}]; a (* Michael De Vlieger, Jan 06 2016 *)

Formula

a(n) = 110*(10^(3*2^(n-3))-1)/999 for n>2. - Bruno Berselli, Jan 29 2016

Extensions

Definition by Michael De Vlieger, Jan 06 2016

Edited by Editors of the OEIS, Jan 29 2016