A067395 First differences of A067368.

4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 2, 2, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2, 4, 4, 4, 4, 4, 4, 4, 2, 2

Offset: 1

Author

John W. Layman, Jan 22 2002

Keywords

• nonn

Comments

See A067396 for the locations of the four consecutive terms {...,4,2,2,4,...} in this sequence.

The asymptotic density of the occurrences of k = 2 and 4 is 1/4 and 3/4, respectively. The asymptotic mean of this sequence is 7/2. - Amiram Eldar, May 31 2024

Crossrefs

Cf. A067368, A067396.

Programs

Python

def A067395(n):
    def iterfun(f,n=0):
        m, k = n, f(n)
        while m != k: m, k = k, f(k)
        return m
    def f(x): return x-sum(((x>>i)-1>>1)+1 for i in range(0,x.bit_length(),3))
    return iterfun(lambda x:f(x)+n+1,n+1)-iterfun(lambda x:f(x)+n,n)<<1 # Chai Wah Wu, Feb 17 2025