A117077 Define binary strings S(0)=0, S(1)=1, S(n) = S(n-2)S(n-1); a(n) = S(n) converted to decimal.

0, 1, 1, 5, 13, 173, 3501, 1420717, 7343549869, 24407739551034797, 264579267653248177273154989, 15107659029337673520218077770654501397966253, 5900314832748922900613950065282124787723453785544193308390237364661677

Offset: 0

Author

Jordan Goldstein (jboymicro20X6(AT)aim.com), Apr 18 2006

Keywords

• base
• nonn

Comments

Note that S(n) in general has leading zeros.

Examples

			S(3) = 01 (base 2) = 1 (base 10) so a(3) = 1.
S(4) = 101 (base 2) = 5 (base 10) so a(4) = 5.
S(5) = 01.101 = 01101 (base 2) = 13 (base 10) so a(5) = 13.
S(6) = 101.01101 = 10101101 (base 2) = 173 (base 10) so a(6) = 173.
S(7) = 01101.10101101 = 0110110101101 (base 2) = 3501 (base 10).
		

Crossrefs

Cf. A063896.

Programs

Mathematica

a[1] = 0; a[2] = 1; a[n_] := a[n] = If[ OddQ@n, FromDigits[ Join[ IntegerDigits[ a[n - 2], 2], IntegerDigits[ a[n - 1], 2]], 2], FromDigits[ Join[ IntegerDigits[ a[n - 2], 2], {0}, IntegerDigits[ a[n - 1], 2]], 2]]; Array[a, 13] (* Robert G. Wilson v, Apr 20 2006 *)

Formula

S(0) = 0, S(1) = 1, so S(2) = 01, a(2) = 1.

Use the substitution system 0->1 and 1->01. The values generated from a(0)=0 are 1, 01, 101, 01101, which in base 10 give the sequence. - Jon Perry, Feb 06 2011

Extensions

More terms from Robert G. Wilson v, Apr 20 2006

Edited by N. J. A. Sloane, Apr 23 2006