This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A180447 #33 Jun 30 2025 04:27:11
%S A180447 0,1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,
%T A180447 4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
%U A180447 6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8
%N A180447 n appears 3n+1 times.
%H A180447 Kevin Ryde, <a href="/A180447/b180447.txt">Table of n, a(n) for n = 0..10000</a>
%F A180447 a(n) = floor((sqrt(24n+1)+1)/6).
%F A180447 a(n) = m+1 if 2n>m*(3m+5) and a(n) = m otherwise where m = floor(sqrt(2n/3)). For n>0, a(n) = k+1 if 2n>=(k+1)(3k+2) and a(n) = k otherwise where k = floor(sqrt(2(n-1)/3)). - _Chai Wah Wu_, Nov 04 2024
%F A180447 Sum_{n>=1} (-1)^(n+1)/a(n) = log(2)/2 (= A016655 / 10). - _Amiram Eldar_, Jun 30 2025
%e A180447 a(5) = floor((sqrt(24*5+1)+1)/6) = 2.
%t A180447 f[n_] := Floor[(Sqrt[24 n + 1] + 1)/6]; Array[f, 105, 0] (* _Robert G. Wilson v_, Sep 10 2010 *)
%o A180447 (Python) l = [floor((sqrt(24*n+1)+1)/6) for n in range(0,101)]
%o A180447 (Python)
%o A180447 from math import isqrt
%o A180447 def A180447(n): return (m:=isqrt((k:=n<<1)//3))+(k>m*(3*m+5)) # _Chai Wah Wu_, Nov 04 2024
%o A180447 (PARI) a(n) = (sqrtint(24*n+1)+1)\6; \\ _Kevin Ryde_, Apr 21 2021
%Y A180447 Cf. A000326 (indices of run starts), A016655, A180446.
%K A180447 easy,nonn
%O A180447 0,6
%A A180447 _William A. Tedeschi_, Sep 07 2010
%E A180447 More terms from _Robert G. Wilson v_, Sep 10 2010