A147757 Palindromes formed from the reflected decimal expansion of the concatenation of 1, 0 and infinite digits 1.

1, 11, 101, 1001, 10101, 101101, 1011101, 10111101, 101111101, 1011111101, 10111111101, 101111111101, 1011111111101, 10111111111101, 101111111111101, 1011111111111101, 10111111111111101, 101111111111111101

Offset: 1

Author

Omar E. Pol, Nov 11 2008

Keywords

• base
• easy
• nonn

Comments

a(n) is also A147758(n) written in base 2.

a(A016789(n)) is divisible by 3 for n > 0. - Altug Alkan, Dec 06 2015

Examples

			n .... Successive digits of a(n)
1 ............. ( 1 )
2 ............ ( 1 1 )
3 ........... ( 1 0 1 )
4 .......... ( 1 0 0 1 )
5 ......... ( 1 0 1 0 1 )
6 ........ ( 1 0 1 1 0 1 )
7 ....... ( 1 0 1 1 1 0 1 )
8 ...... ( 1 0 1 1 1 1 0 1 )
9 ..... ( 1 0 1 1 1 1 1 0 1 )
10 ... ( 1 0 1 1 1 1 1 1 0 1 )
		

Links

• Index entries for linear recurrences with constant coefficients, signature (11,-10).

Crossrefs

Cf. A000533, A016789, A135577, A138120, A138144, A138145, A138146, A138721, A138826, A147758.

Cf. A144564 (a bisection).

Programs

Mathematica

f[n_] := Block[{w = {1, 0}}, Which[n == 1, w = {1}, n == 2, w = {1, 1}, n == 3, AppendTo[w, 1], n >= 4, w = Join[w, Table[1, {n - 4}], Reverse@ w]]; FromDigits@ w]; Array[f, 19] (* Michael De Vlieger, Dec 05 2015 *)
LinearRecurrence[{11,-10},{1,11,101,1001,10101},20] (* Harvey P. Dale, Aug 02 2017 *)

PARI

Vec( x+11*x^2+101*x^3 -91*x^4*(-11+10*x) / ( (10*x-1)*(x-1) ) + O(x^30)) \\ Michel Marcus, Dec 05 2015

Formula

G.f.: x+11*x^2+101*x^3-91*x^4*(-11+10*x) / ( (10*x-1)*(x-1) ). - R. J. Mathar, Aug 24 2011

a(n) = 11*a(n-1) - 10*a(n-2) for n>2. Wesley Ivan Hurt, Dec 06 2015