A363089 Positive numbers k for which cos(k) > sin(k).

4, 5, 6, 7, 11, 12, 13, 17, 18, 19, 23, 24, 25, 30, 31, 32, 36, 37, 38, 42, 43, 44, 48, 49, 50, 51, 55, 56, 57, 61, 62, 63, 67, 68, 69, 74, 75, 76, 80, 81, 82, 86, 87, 88, 92, 93, 94, 95, 99, 100, 101, 105, 106, 107, 111, 112, 113, 118, 119, 120, 124, 125, 126, 130, 131, 132

Offset: 1

Author

Wolfe Padawer, May 18 2023

Keywords

• nonn

Comments

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.

Positive numbers k such that frac(3/8 + k/(2 * Pi)) < 1/2. - Robert Israel, Jun 18 2024

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Complement of A363088.

Programs

Maple

filter:= k -> is(frac(k/(2*Pi) + 3/8) < 1/2):
select(filter, [$1..200]); # Robert Israel, Jun 18 2024