A379265 - OEIS

%I #22 Jan 11 2025 03:59:21

%S 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 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 8,8,9,9,10,11,12,13,13,14,14,14,14,14,15

%N 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 a(n) appears to grow roughly like sqrt(n).

%H Pontus von Brömssen, <a href="/A379265/b379265.txt">Table of n, a(n) for n = 0..9999</a>

%H Pontus von Brömssen, <a href="/A379265/a379265.png">Plot of A379265(n), A379266(n), and sqrt(n) for n=0..100000</a>.

%F For n >= 1, a(n) = a(n-1)+1 if a(n-1) = A379266(n-1), otherwise a(n) = a(n-1).

%o (Python)

%o def A379265_list(nterms):

%o     A = []

%o     A379266 = []

%o     for n in range(nterms):

%o         if n != 0:

%o             a += (a==A379266[-1])

%o         else:

%o             a = 0

%o         b = sum(1 for x,y in zip(A,reversed(A379266)) if x==y)

%o         A.append(a)

%o         A379266.append(b)

%o     return A

%Y Cf. A272727, A379266, A379297.

%K nonn,changed

%O 0,3

%A _Pontus von Brömssen_, Dec 19 2024