The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A038573 a(n) = 2^A000120(n) - 1. 35
 0, 1, 1, 3, 1, 3, 3, 7, 1, 3, 3, 7, 3, 7, 7, 15, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 3, 7, 7, 15, 7, 15, 15, 31, 7, 15, 15, 31, 15, 31, 31, 63, 1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31, 3, 7, 7, 15, 7, 15, 15, 31 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Essentially the same sequence as A001316, which has much more information, and also A159913. - N. J. A. Sloane, Jun 05 2009 Smallest number with same number of 1's in its binary expansion as n. Fixed point of the morphism 0 -> 01, 1 -> 13, 3 -> 37, ... = k -> k, 2k+1, ... starting from a(0) = 0; 1 -> 01 -> 0113 -> 01131337 -> 011313371337377(15) -> ..., . - Robert G. Wilson v, Jan 24 2006 From Gary W. Adamson, Jun 04 2009: (Start) As an infinite string, 2^n terms per row starting with "1": (1; 1,3; 1,3,3,7; 1,3,3,7,3,7,7,15; 1,3,3,7,3,7,7,15,3,7,7,15,7,15,15,3l;...) Row sums of that triangle = A027649: (1, 4, 14, 46, 454, ...); where the next row sum = current term of A027649 + next term in finite difference row of A027649, i.e., (1, 3, 10, 32, 100, 308, ...) = A053581. (End) From Omar E. Pol, Jan 24 2016: (Start) Partial sums give A267700. a(n) is also the number of cells turned ON at n-th generation of the cellular automaton of A267700 in a 90-degree sector on the square grid. a(n) is also the number of Y-toothpicks added at n-th generation of the structure of A267700 in a 120-degree sector on the triangular grid. (End) LINKS Seiichi Manyama, Table of n, a(n) for n = 0..8191 (terms 0..1023 from T. D. Noe) David Applegate, The movie version Michael Gilleland, Some Self-Similar Integer Sequences N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS FORMULA a(2n) = a(n), a(2n+1) = 2*a(n)+1, a(0) = 0. a(n) = A001316(n)-1 = 2^A000120(n) - 1. - Daniele Parisse (daniele.parisse(AT)m.dasa.de) a(n) = number of positive integers k < n such that n XOR k = n-k (cf. A115378). - Paul D. Hanna, Jan 21 2006 a(n) = f(n, 1) with f(x, y) = if x = 0 then y - 1 else f(floor(x/2), y*(1 + x mod 2)). - Reinhard Zumkeller, Nov 21 2009 a(n) = (n mod 2 + 1) * a(floor(n/2)) + n mod 2. - Reinhard Zumkeller, Oct 10 2012 a(n) = Sum_{i=1..n} C(n,i) mod 2. - Wesley Ivan Hurt, Nov 17 2017 G.f.: -1/(1 - x) + Product_{k>=0} (1 + 2*x^(2^k)). - Ilya Gutkovskiy, Aug 20 2019 EXAMPLE 9 = 1001 -> 0011 -> 3, so a(9)=3. From Gary W. Adamson, Jun 04 2009: (Start) Triangle read by rows:   1;   1, 3;   1, 3, 3, 7;   1, 3, 3, 7, 3, 7, 7, 15;   1, 3, 3, 7, 3, 7, 7, 15, 3, 7, 7, 15, 7, 15, 15, 31;   ... Row sums: (1, 4, 14, 46, ...) = A026749 = last row terms + new set of terms such that row 3 = (1, 3, 3, 7,) + (3, 7, 7, 15) = 14 + 32 = A027649(3) + A053581(3). (End) The rows of this triangle converge to A159913. - N. J. A. Sloane, Jun 05 2009 MAPLE seq(2^convert(convert(n, base, 2), `+`)-1, n=0..100); # Robert Israel, Jan 24 2016 MATHEMATICA Array[ 2^Count[ IntegerDigits[ #, 2 ], 1 ]-1&, 100 ] Nest[ Flatten[ # /. a_Integer -> {a, 2a + 1}] &, {0}, 7] (* Robert G. Wilson v, Jan 24 2006 *) PROG (PARI) a(n)=2^subst(Pol(binary(n)), x, 1)-1 (PARI) a(n) = 2^hammingweight(n)-1; \\ Michel Marcus, Jan 24 2016 (Haskell) a038573 0 = 0 a038573 n = (m + 1) * (a038573 n') + m where (n', m) = divMod n 2 -- Reinhard Zumkeller, Oct 10 2012, Feb 07 2011 CROSSREFS Cf. A007313, A115378. This is Guy Steele's sequence GS(3, 6) (see A135416). Cf. also A000079, A001316, A027649, A053581, A159913, A267700. Write n in b-ary, sort digits into increasing order: this sequence (b=2), A038574 (b=3), A319652 (b=4), A319653 (b=5), A319654 (b=6), A319655 (b=7), A319656 (b=8), A319657 (b=9), A004185 (b=10). Column k=0 of A340666. Sequence in context: A333334 A205145 A061892 * A246591 A173465 A151837 Adjacent sequences:  A038570 A038571 A038572 * A038574 A038575 A038576 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from Erich Friedman New definition from N. J. A. Sloane, Mar 01 2008 STATUS approved

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

Last modified May 15 08:59 EDT 2021. Contains 343909 sequences. (Running on oeis4.)