OFFSET
1,2
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.
MATHEMATICA
Select[Range[200], Sin[# - Pi/4] > 0 &] (* Vaclav Kotesovec, Jul 01 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Wolfe Padawer, May 18 2023
STATUS
approved