A182028 - OEIS

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

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OFFSET

0,3

COMMENTS

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

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

LINKS

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

FORMULA

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

EXAMPLE

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.

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 *)

PROG

(Haskell)

a182028 n = a182028_list !! n

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

CROSSREFS

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

Sequence in context: A056185 A363262 A152537 * A081253 A118255 A206927

Adjacent sequences: A182025 A182026 A182027 * A182029 A182030 A182031

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Apr 07 2012

STATUS

approved