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 A363089 #16 Jun 19 2024 02:03:09 %S A363089 4,5,6,7,11,12,13,17,18,19,23,24,25,30,31,32,36,37,38,42,43,44,48,49, %T A363089 50,51,55,56,57,61,62,63,67,68,69,74,75,76,80,81,82,86,87,88,92,93,94, %U A363089 95,99,100,101,105,106,107,111,112,113,118,119,120,124,125,126,130,131,132 %N A363089 Positive numbers k for which cos(k) > sin(k). %C A363089 Terms of this sequence come in groups of 3 or 4 consecutive integers, with spaces between them of length 3 or 4. This is a direct consequence of the fact that 3 < Pi < 4. Across the entire infinite sequence, the percentage of groups of consecutive integers that have 4 members (and the percentage of spaces that are of length 4) is (Pi - 3)*100% = 14.1592653589...%. In the integers between 1 and 10^12, there are 159154943092 groups, of which 22535170724 are length 4, a percentage of 14.1592653587...%, which matches Pi to 11 decimal places. %C A363089 Positive numbers k such that frac(3/8 + k/(2 * Pi)) < 1/2. - _Robert Israel_, Jun 18 2024 %H A363089 Robert Israel, <a href="/A363089/b363089.txt">Table of n, a(n) for n = 1..10000</a> %p A363089 filter:= k -> is(frac(k/(2*Pi) + 3/8) < 1/2): %p A363089 select(filter, [$1..200]); # _Robert Israel_, Jun 18 2024 %Y A363089 Complement of A363088. %K A363089 nonn %O A363089 1,1 %A A363089 _Wolfe Padawer_, May 18 2023