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

Author

Ali Sada, Aug 14 2019

Keywords

• nonn
• base
• easy

Comments

All terms are even.

Examples

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

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

Crossrefs

Cf. A000120, A048725, A112627.

Cf. also A007302, A069010.

Programs

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 *)

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

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