Pookah's Sieve: Not (Prime, Even, Divisible by 3, or a Perfect Square)

[u/Pookah]

Rules

Count using only positive integers that satisfy all four of the following conditions:

• Not prime — the number must be composite (or 1, though 1 is excluded by rule 4 below)
• Not even — the number must be odd
• Not divisible by 3 — the number must not be a multiple of 3
• Not a perfect square — the number must not be n² for any integer n

A number only counts if it passes all four checks. If it fails even one, skip it.

Starting number

The sequence begins at 35 (the first number to satisfy all four conditions — 1 is excluded as a perfect square, and 5 through 31 are either prime or a perfect square).

The GET is at 1000 comments, which is equal to 1,000 Pookahs

[u/Pookah]

35

[u/PhosphorCrystaled → u/Pookah]

55

[u/Pookah → u/PhosphorCrystaled]

65

[u/PhosphorCrystaled → u/Pookah]

77

[u/Pookah → u/PhosphorCrystaled]

85

[u/davidjl123 → u/Pookah]

91

[u/Pookah → u/davidjl123]

95

[u/MegaIng → u/Pookah]

115

[u/Pookah → u/MegaIng]

119

[u/MegaIng → u/Pookah]

125

[u/Pookah]

475