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!)
 A139351 Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k's that are even, o(n) the number that are odd; sequence gives e(n). 15
 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 3, 2, 3, 1, 2, 1, 2, 2, 3, 2, 3, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 3, 2, 3, 1, 2, 1, 2, 2, 3, 2, 3, 1, 2, 1, 2, 2, 3, 2, 3, 1, 2, 1, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 4, 3, 4, 2, 3, 2, 3, 3, 4, 3, 4, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS e(n)+o(n) = A000120(n), the binary weight of n. a(n) is also number of 1's and 3's in 4-ary representation of n. - Frank Ruskey, May 02 2009 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 F. T. Adams-Watters, F. Ruskey, Generating Functions for the Digital Sum and Other Digit Counting Sequences, JIS 12 (2009) 09.5.6 N. J. A. Sloane, Fortran program for this and related sequences FORMULA a(n) + A139352(n) = A000120(n). G.f.: (1/(1-z))*Sum_{m>=0} (z^(4^m)/(1+z^(4^m))). - Frank Ruskey, May 03 2009 Recurrence relation: a(0)=0, a(4m) = a(4m+2) = a(m), a(4m+1) = a(4m+3) = 1+a(m). - Frank Ruskey, May 11 2009 a(n) = Sum_{k} A030308(n,k)*A059841(k). - Philippe Deléham, Oct 14 2011 EXAMPLE For n = 43 = 2^0 + 2^1 + 2^3 + 2^5, e(43)=1, o(43)=3. MAPLE A139351 := proc(n)     local a, bdgs, r;     a := 0 ;     bdgs := convert(n, base, 2) ;     for r from 1 to nops(bdgs) by 2 do         if op(r, bdgs) = 1 then             a := a+1 ;         end if;     end do:     a; end proc: # R. J. Mathar, Jul 21 2016 MATHEMATICA terms = 99; s = (1/(1-z))*Sum[z^(4^m)/(1+z^(4^m)), {m, 0, Log[4, terms] // Ceiling}] + O[z]^terms; CoefficientList[s, z] (* Jean-François Alcover, Jul 21 2017 *) PROG (Fortran) See Sloane link. (Haskell) import Data.List (unfoldr) a139351 = sum . map (`mod` 2) .    unfoldr (\x -> if x == 0 then Nothing else Just (x, x `div` 4) -- Reinhard Zumkeller, Apr 22 2011 (PARI) a(n)=if(n>3, a(n\4))+n%2 \\ Charles R Greathouse IV, Apr 21 2016 CROSSREFS Cf. A000120, A139352-A139355, A039004, A139370-A139373. Sequence in context: A131851 A104886 A215604 * A285677 A036578 A229764 Adjacent sequences:  A139348 A139349 A139350 * A139352 A139353 A139354 KEYWORD nonn,easy AUTHOR Nadia Heninger and N. J. A. Sloane, Jun 07 2008 EXTENSIONS Typo in example fixed by Reinhard Zumkeller, Apr 22 2011 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 January 21 12:38 EST 2021. Contains 340350 sequences. (Running on oeis4.)