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A379265 a(n) is the number of coincidences of the first n terms of this sequence and A379266, i.e., the number of equalities a(k) = A379266(k) for 0 <= k < n.

%I A379265 #22 Jan 11 2025 03:59:21
%S A379265 0,1,2,2,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,6,6,6,6,
%T A379265 6,6,6,6,6,6,6,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
%U A379265 8,8,9,9,10,11,12,13,13,14,14,14,14,14,15
%N A379265 a(n) is the number of coincidences of the first n terms of this sequence and A379266, i.e., the number of equalities a(k) = A379266(k) for 0 <= k < n.
%C A379265 a(n) appears to grow roughly like sqrt(n).
%H A379265 Pontus von Brömssen, <a href="/A379265/b379265.txt">Table of n, a(n) for n = 0..9999</a>
%H A379265 Pontus von Brömssen, <a href="/A379265/a379265.png">Plot of A379265(n), A379266(n), and sqrt(n) for n=0..100000</a>.
%F A379265 For n >= 1, a(n) = a(n-1)+1 if a(n-1) = A379266(n-1), otherwise a(n) = a(n-1).
%o A379265 (Python)
%o A379265 def A379265_list(nterms):
%o A379265     A = []
%o A379265     A379266 = []
%o A379265     for n in range(nterms):
%o A379265         if n != 0:
%o A379265             a += (a==A379266[-1])
%o A379265         else:
%o A379265             a = 0
%o A379265         b = sum(1 for x,y in zip(A,reversed(A379266)) if x==y)
%o A379265         A.append(a)
%o A379265         A379266.append(b)
%o A379265     return A
%Y A379265 Cf. A272727, A379266, A379297.
%K A379265 nonn
%O A379265 0,3
%A A379265 _Pontus von Brömssen_, Dec 19 2024