A067396 - OEIS

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

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OFFSET

1,1

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

LINKS

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

EXAMPLE

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

PROG

(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)