A363088 - OEIS

%I #16 Jul 04 2023 23:55:34

%S 1,2,3,8,9,10,14,15,16,20,21,22,26,27,28,29,33,34,35,39,40,41,45,46,

%T 47,52,53,54,58,59,60,64,65,66,70,71,72,73,77,78,79,83,84,85,89,90,91,

%U 96,97,98,102,103,104,108,109,110,114,115,116,117,121,122,123,127,128,129

%N Positive numbers k for which sin(k) >= cos(k).

%C Terms of the 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 22535170725 are of length 4, a percentage of 14.1592653594...%, which matches Pi to 10 decimal places.

%t Select[Range[200], Sin[# - Pi/4] > 0 &] (* _Vaclav Kotesovec_, Jul 01 2023 *)

%Y Complement of A363089.

%K nonn

%O 1,2

%A _Wolfe Padawer_, May 18 2023