A309709 Number of binary digits that change when n is multiplied by 4.

0, 2, 2, 4, 2, 2, 4, 4, 2, 4, 2, 4, 4, 4, 4, 4, 2, 4, 4, 6, 2, 2, 4, 4, 4, 6, 4, 6, 4, 4, 4, 4, 2, 4, 4, 6, 4, 4, 6, 6, 2, 4, 2, 4, 4, 4, 4, 4, 4, 6, 6, 8, 4, 4, 6, 6, 4, 6, 4, 6, 4, 4, 4, 4, 2, 4, 4, 6, 4, 4, 6, 6, 4, 6, 4, 6, 6, 6, 6, 6, 2, 4, 4, 6, 2, 2, 4, 4

Offset

0,2

Comments

All terms are even.

Links

David A. Corneth, Table of n, a(n) for n = 0..9999

Joerg Arndt, Matters Computational (The Fxtbook)

Index entries for sequences related to binary expansion of n

Formula

a(n) = A000120(A048725(n)). - Antti Karttunen, Aug 22 2019

a(A112627(n)) = 2*n and A112627(n) is the first position where 2*n occurs in this sequence. - David A. Corneth, Sep 19 2019

Example

00101_2 * 100_2 = 10100_2: 2 bits changed, so a(5) = 2.

Maple

a:= n-> add(i, i=Bits[Split](Bits[Xor](n*4, n))):
seq(a(n), n=0..120);  # Alois P. Heinz, Aug 23 2019

Mathematica

a[n_] := Total@ IntegerDigits[BitXor[n, 4 n], 2]; Array[a, 88, 0] (* Giovanni Resta, Sep 19 2019 *)

Prog

(PARI) A309709(n) = hammingweight(bitxor(n, n<<2)); \\ Antti Karttunen, Aug 22 2019
(Python)
def A309709(n):
    s = ""
    while n > 0:
        s, n = str(n%2)+s, n//2
    s, s4, i, j = "00"+s, s+"00", 0, 0
    while i < len(s):
        if s[i] != s4[i]:
            j = j+1
        i = i+1
    return j # A.H.M. Smeets, Aug 23 2019

Crossrefs

Cf. A000120, A048725, A112627.

Cf. also A007302, A069010.

Sequence in context: A087692 A093621 A242734 * A143230 A276604 A072301

Adjacent sequences: A309706 A309707 A309708 * A309710 A309711 A309712

Keyword

nonn,base,easy

Author

Ali Sada, Aug 14 2019

Status

approved