A067396 a(n) is the position of the n-th occurrence of the pair "2,2" in A067395 (the first difference sequence of A067368).

4, 13, 22, 31, 36, 41, 50, 59, 68, 77, 86, 95, 104, 109, 114, 123, 132, 141, 150, 159, 168, 177, 182, 187, 196, 205, 214, 223, 232, 241, 250, 255, 260, 269, 278, 287, 292, 297, 306, 315, 324, 329, 334, 343, 352, 361, 370, 379, 388, 397, 402, 407, 416, 425

Offset: 1

Author

John W. Layman, Jan 22 2002

Keywords

• nonn

Comments

A comparison of this sequence with A067368 suggests the following conjecture: a(n)=2*A067368(n)+n-1. This has been confirmed for several hundred terms.

Above conjecture is true, and it is same as conjecture in Formula section of A067368. - Altug Alkan, Sep 26 2018

The asymptotic density of this sequence is 1/8. - Amiram Eldar, May 31 2024

Examples

			A067395 begins {4,4,4,2,2,4,4,4,4,...}, so a(1)=4.
		

Links

• Altug Alkan, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A067368, A067395, A213258.

Programs

Python

def A067396(n):
    def f(x): return n+x-sum(((x>>i)-1>>1)+1 for i in range(0,x.bit_length(),3))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return (m<<2)+n-1 # Chai Wah Wu, Feb 17 2025