login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A159918 Number of ones in binary representation of n^2. 23
0, 1, 1, 2, 1, 3, 2, 3, 1, 3, 3, 5, 2, 4, 3, 4, 1, 3, 3, 5, 3, 6, 5, 3, 2, 5, 4, 6, 3, 5, 4, 5, 1, 3, 3, 5, 3, 6, 5, 7, 3, 5, 6, 7, 5, 8, 3, 4, 2, 5, 5, 5, 4, 8, 6, 7, 3, 6, 5, 7, 4, 6, 5, 6, 1, 3, 3, 5, 3, 6, 5, 7, 3, 6, 6, 9, 5, 7, 7, 5, 3, 6, 5, 8, 6, 7, 7, 7, 5, 9, 8, 5, 3, 6, 4, 5, 2, 5, 5, 6, 5, 9, 5, 7, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The binary weight (A000120) of n^2.

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..10000

Bernt Lindström, On the binary digits of a power, Journal of Number Theory, Volume 65, Issue 2, August 1997, Pages 321-324.

K. B. Stolarsky, The binary digits of a power, Proc. Amer. Math. Soc. 71 (1978), 1-5.

FORMULA

a(n) = A000120(A000290(n)); a(A077436(n)) = A000120(A077436(n)).

Lindström shows that lim sup wt(m^2)/log_2 m = 2. - N. J. A. Sloane, Oct 11 2013

MAPLE

A159918 := proc(n) return add(b, b=convert(n^2, base, 2)): end: seq(A159918(n), n=0..100); # Nathaniel Johnston, Jun 23 2011

PROG

(Haskell)

a159918 = a000120 . a000290  -- Reinhard Zumkeller, Oct 12 2013

(Python)

def A159918(n):

....return bin(n*n).count('1') # Chai Wah Wu, Sep 03 2014

(PARI) a(n)=hammingweight(n^2) \\ Charles R Greathouse IV, Aug 06 2015

CROSSREFS

Cf. A000120, A007088, A192085, A004159, A214560, A231897, A231898. For records see A230097.

Sequence in context: A107337 A066376 A151682 * A278573 A108663 A057940

Adjacent sequences:  A159915 A159916 A159917 * A159919 A159920 A159921

KEYWORD

nonn,base,easy

AUTHOR

Reinhard Zumkeller, Apr 25 2009

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 20 16:25 EST 2018. Contains 299380 sequences. (Running on oeis4.)