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A022290 Replace 2^k in binary expansion of n with Fibonacci(k+2). 11
0, 1, 2, 3, 3, 4, 5, 6, 5, 6, 7, 8, 8, 9, 10, 11, 8, 9, 10, 11, 11, 12, 13, 14, 13, 14, 15, 16, 16, 17, 18, 19, 13, 14, 15, 16, 16, 17, 18, 19, 18, 19, 20, 21, 21, 22, 23, 24, 21, 22, 23, 24, 24, 25, 26, 27, 26, 27, 28, 29, 29, 30, 31, 32, 21, 22, 23, 24, 24, 25, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: 1/(1-x) * Sum_{k>=0} F(k+2)*x^2^k/(1+x^2^k), where F = A000045.

a(n) = Sum_{k>=0} A030308(n,k)*A000045(k+2). - Philippe Deléham, Oct 15 2011

a(A003714(n)) = n. - R. J. Mathar, Jan 31 2015

a(A000225(n)) = A001911(n). - Philippe Deléham, Jun 05 2015

From Jeffrey Shallit, Jul 17 2018: (Start)

Can be computed from the recurrence:

a(4*k)   = a(k)+a(2*k),

a(4*k+1) = a(k)+a(2*k+1),

a(4*k+2) = a(k)-a(2*k)+2*a(2*k+1),

a(4*k+3) = a(k)-2*a(2*k)+3*a(2*k+1),

and the initial terms a(0) = 0, a(1) = 1. (End)

EXAMPLE

n=4 = 2^2 is replaced by A000045(2+2) =3. n=5 =2^2+2^0 is replaced by A000045(2+2)+A000045(0+2) = 3+1=4. - R. J. Mathar, Jan 31 2015

This sequence regarded as a triangle with rows of lengths 1, 1, 2, 4, 8, 16, ...:

0

1

2, 3

3, 4, 5, 6

5, 6, 7, 8, 8, 9, 10, 11

8, 9, 10, 11, 11, 12, 13, 14, 13, 14, 15, 16, 16, 17, 18, 19

... - Philippe Deléham, Jun 05 2015

MAPLE

A022290 := proc(n)

    dgs := convert(n, base, 2) ;

    add( op(i, dgs)*A000045(i+1), i=1..nops(dgs)) ;

end proc: # R. J. Mathar, Jan 31 2015

MATHEMATICA

Table[Reverse[#].Fibonacci[1 + Range[Length[#]]] &@ IntegerDigits[n, 2], {n, 0, 54}] (* IWABUCHI Yu(u)ki, Aug 01 2012 *)

PROG

(Haskell)

a022290 0 = 0

a022290 n = h n 0 $ drop 2 a000045_list where

   h 0 y _      = y

   h x y (f:fs) = h x' (y + f * r) fs where (x', r) = divMod x 2

-- Reinhard Zumkeller, Oct 03 2012

CROSSREFS

Other sequences that are built by replacing 2^k in the binary representation with other numbers: A029931 (naturals), A059590 (factorials), A089625 (primes).

Sequence in context: A029931 A290801 A244041 * A185363 A103827 A094182

Adjacent sequences:  A022287 A022288 A022289 * A022291 A022292 A022293

KEYWORD

nonn,tabf

AUTHOR

Marc LeBrun

STATUS

approved

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Last modified October 22 09:13 EDT 2018. Contains 316433 sequences. (Running on oeis4.)