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

0,4

Comments

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

Links

Table of n, a(n) for n=0..12.

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

Example

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).

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 *)

Crossrefs

Cf. A063896.

Sequence in context: A187894 A214591 A159261 * A124924 A209271 A352083

Adjacent sequences: A117074 A117075 A117076 * A117078 A117079 A117080

Keyword

base,nonn

Author

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

Extensions

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

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

Status

approved