cp's OEIS Frontend

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.

A180446 Number of non-pentagonal numbers <= n.

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%I A180446 #16 Nov 05 2024 12:18:32
%S A180446 0,0,1,2,3,3,4,5,6,7,8,9,9,10,11,12,13,14,15,16,17,18,18,19,20,21,22,
%T A180446 23,24,25,26,27,28,29,30,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,
%U A180446 45,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,63,64,65,66
%N A180446 Number of non-pentagonal numbers <= n.
%H A180446 Harvey P. Dale, <a href="/A180446/b180446.txt">Table of n, a(n) for n = 0..1000</a>
%F A180446 a(n) = n - floor((sqrt(24n+1)+1)/6) = n - A180447(n).
%e A180446 a(5) = 5 - floor((sqrt(24*5+1)+1)/6) = 3.
%t A180446 f[n_] := n - Floor[(Sqrt[24 n + 1] + 1)/6]; Array[f, 74, 0] (* _Robert G. Wilson v_, Sep 10 2010 *)
%t A180446 Accumulate[Table[If[IntegerQ[(1+Sqrt[1+24n])/6],0,1],{n,0,80}]]-1 (* _Harvey P. Dale_, May 22 2023 *)
%o A180446 (Python) l = [n-floor((sqrt(24*n+1)+1)/6) for n in range(0,101)]
%o A180446 (Python)
%o A180446 from math import isqrt
%o A180446 def A180446(n): return n-(m:=isqrt((k:=n<<1)//3))-(k>m*(3*m+5)) # _Chai Wah Wu_, Nov 04 2024
%K A180446 easy,nonn
%O A180446 0,4
%A A180446 _William A. Tedeschi_, Sep 07 2010
%E A180446 More terms from _Robert G. Wilson v_, Sep 10 2010