Pi is good because it's 3.x. e is good because it's 2.x. If you need a 1.x, then the next obvious is phi (the golden ratio), 1.618.

You could use square roots of 2, 3, 5 for 1.414, 1.732 and 2.236.

Others that look good are Sierpiński's constant is 2.585, Lévy's constant is 3.276, Feigenbaum constants of 4.669 or 2.503.

Wade.