The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A022290 Replace 2^k in binary expansion of n with Fibonacci(k+2). 39
 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) a(A003754(n)) = n-1. - Rémy Sigrist, Jan 28 2020 From Rémy Sigrist, Aug 04 2022: (Start) Empirically: - a(2*A003714(n)) = A022342(n+1), - a(3*A003714(n)) = a(4*A003714(n)) = A026274(n) for n > 0. (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 From Philippe Deléham, Jun 05 2015: (Start) 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 ... (End) 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 # second Maple program: b:= (n, i, j)-> `if`(n=0, 0, j*irem(n, 2, 'q')+b(q, j, i+j)): a:= n-> b(n, 1\$2): seq(a(n), n=0..127); # Alois P. Heinz, Jan 26 2022 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 (PARI) my(m=Mod('x, 'x^2-'x-1)); a(n) = subst(lift(subst(Pol(binary(n)), 'x, m)), 'x, 2); \\ Kevin Ryde, Sep 22 2020 (Python) def A022290(n): a, b, s = 1, 2, 0 for i in bin(n)[-1:1:-1]: s += int(i)*a a, b = b, a+b return s # Chai Wah Wu, Sep 10 2022 CROSSREFS Other sequences that are built by replacing 2^k in the binary representation with other numbers: A029931 (naturals), A054204 (even-indexed Fibonacci numbers), A062877 (odd-indexed Fibonacci numbers), A059590 (factorials), A089625 (primes). Cf. A003754, A022342, A026274. Sequence in context: A322815 A244041 A331835 * A344350 A185363 A103827 Adjacent sequences: A022287 A022288 A022289 * A022291 A022292 A022293 KEYWORD nonn,tabf,base AUTHOR Marc LeBrun STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 3 19:58 EDT 2024. Contains 374909 sequences. (Running on oeis4.)