A182028 Take first n bits of the infinite Fibonacci word A003849, regard them as a binary number, then convert it to base 10.

0, 1, 2, 4, 9, 18, 37, 74, 148, 297, 594, 1188, 2377, 4754, 9509, 19018, 38036, 76073, 152146, 304293, 608586, 1217172, 2434345, 4868690, 9737380, 19474761, 38949522, 77899045, 155798090, 311596180, 623192361, 1246384722, 2492769444, 4985538889, 9971077778

Offset: 0

Author

Reinhard Zumkeller, Apr 07 2012

Keywords

• nonn
• base

Comments

a(n) mod 2 = A003849(n);

a(n) = A000225(n+1) - A044432(n).

Examples

			0 ->                            0 -> a(0) = 0,
0,1 ->                         01 -> a(1) = 1,
0,1,0 ->                      010 -> a(2) = 2,
0,1,0,0 ->                   0100 -> a(3) = 4,
0,1,0,0,1 ->                01001 -> a(4) = 9,
0,1,0,0,1,0 ->             010010 -> a(5) = 18,
0,1,0,0,1,0,1 ->          0100101 -> a(6) = 37
0,1,0,0,1,0,1,0 ->       01001010 -> a(7) = 74
0,1,0,0,1,0,1,0,0 ->    010010100 -> a(8) = 148,
0,1,0,0,1,0,1,0,0,1 -> 0100101001 -> a(9) = 297.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A003842, A003849, A000225, A044432, A214318.

Programs

Haskell

a182028 n = a182028_list !! n
a182028_list = scanl1 (\v b -> 2 * v + b) a003849_list

Mathematica

nesting = 7; A003849 = Flatten[Nest[{#, #[[1]]}&, {0, 1}, nesting]]; a[n_] := FromDigits[Take[A003849, n+1], 2]; Table[a[n], {n, 0, Length[A003849] - 1}] (* Jean-François Alcover, Feb 13 2016 *)

Formula

a(n) = 2*a(n-1) + A003849(n) for n > 0, a(0) = 0.