OFFSET
1,1
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
MAPLE
filter:= k -> is(frac(k/(2*Pi) + 3/8) < 1/2):
select(filter, [$1..200]); # Robert Israel, Jun 18 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Wolfe Padawer, May 18 2023
STATUS
approved