cp's OEIS Frontend

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

%I A067396 #20 Feb 18 2025 08:59:02
%S A067396 4,13,22,31,36,41,50,59,68,77,86,95,104,109,114,123,132,141,150,159,
%T A067396 168,177,182,187,196,205,214,223,232,241,250,255,260,269,278,287,292,
%U A067396 297,306,315,324,329,334,343,352,361,370,379,388,397,402,407,416,425
%N A067396 a(n) is the position of the n-th occurrence of the pair "2,2" in A067395 (the first difference sequence of A067368).
%C A067396 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.
%C A067396 Above conjecture is true, and it is same as conjecture in Formula section of A067368. - _Altug Alkan_, Sep 26 2018
%C A067396 The asymptotic density of this sequence is 1/8. - _Amiram Eldar_, May 31 2024
%H A067396 Altug Alkan, <a href="/A067396/b067396.txt">Table of n, a(n) for n = 1..1000</a>
%e A067396 A067395 begins {4,4,4,2,2,4,4,4,4,...}, so a(1)=4.
%o A067396 (Python)
%o A067396 def A067396(n):
%o A067396     def f(x): return n+x-sum(((x>>i)-1>>1)+1 for i in range(0,x.bit_length(),3))
%o A067396     m, k = n, f(n)
%o A067396     while m != k: m, k = k, f(k)
%o A067396     return (m<<2)+n-1 # _Chai Wah Wu_, Feb 17 2025
%Y A067396 Cf. A067368, A067395, A213258.
%K A067396 nonn
%O A067396 1,1
%A A067396 _John W. Layman_, Jan 22 2002