A363088 Positive numbers k for which sin(k) >= cos(k).

1, 2, 3, 8, 9, 10, 14, 15, 16, 20, 21, 22, 26, 27, 28, 29, 33, 34, 35, 39, 40, 41, 45, 46, 47, 52, 53, 54, 58, 59, 60, 64, 65, 66, 70, 71, 72, 73, 77, 78, 79, 83, 84, 85, 89, 90, 91, 96, 97, 98, 102, 103, 104, 108, 109, 110, 114, 115, 116, 117, 121, 122, 123, 127, 128, 129

Offset: 1

Author

Wolfe Padawer, May 18 2023

Keywords

• nonn

Comments

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.

Crossrefs

Complement of A363089.

Programs

Mathematica

Select[Range[200], Sin[# - Pi/4] > 0 &] (* Vaclav Kotesovec, Jul 01 2023 *)