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A214560 Number of 0's in binary expansion of n^2. 5
1, 0, 2, 2, 4, 2, 4, 3, 6, 4, 4, 2, 6, 4, 5, 4, 8, 6, 6, 4, 6, 3, 4, 7, 8, 5, 6, 4, 7, 5, 6, 5, 10, 8, 8, 6, 8, 5, 6, 4, 8, 6, 5, 4, 6, 3, 9, 8, 10, 7, 7, 7, 8, 4, 6, 5, 9, 6, 7, 5, 8, 6, 7, 6, 12, 10, 10, 8, 10, 7, 8, 6, 10, 7, 7, 4, 8, 6, 6, 8, 10, 7, 8, 5, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Conjecture: for every x>=0 there is an i such that a(n)>x for n>i.

Comment from N. J. A. Sloane, Nov 21 2013: See also the conjecture in A231898.

LINKS

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

FORMULA

a(n) = A023416(A000290(n)).

MAPLE

A214560 := proc(n)

    A023416(n^2) ;

end proc: # R. J. Mathar, Jul 21 2012

PROG

(Python)

for n in range(300):

    b = n*n

    c = 0

    while b>0:

        c += 1-(b&1)

        b/=2

    print c+(n==0),

(PARI) vector(66, n, b=binary((n-1)^2); sum(j=1, #b, 1-b[j])) /* Joerg Arndt, Jul 21 2012 */

(Haskell)

a214560 = a023416 . a000290  -- Reinhard Zumkeller, Nov 20 2013

(Python)

def A214560(n):

....return bin(n*n)[2:].count('0') # Chai Wah Wu, Sep 03 2014

CROSSREFS

Cf. A000120, A023416, A078565, A159918, A231898.

Sequence in context: A318476 A226083 A182730 * A152858 A091248 A082991

Adjacent sequences:  A214557 A214558 A214559 * A214561 A214562 A214563

KEYWORD

base,nonn

AUTHOR

Alex Ratushnyak, Jul 21 2012

STATUS

approved

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Last modified June 19 10:32 EDT 2019. Contains 324219 sequences. (Running on oeis4.)