Chapter 4: Systems Based on Numbers

Section 5: Mathematical Constants

Specially constructed transcendental numbers

Numbers known to be transcendental include ones whose digit sequences contain 1's only at positions n!, 2^n or Fibonacci[n]. Concatenation sequences, as well as generalizations formed by concatenating values of polynomials at successive integer points, are also known to yield numbers that are transcendental.

From Stephen Wolfram: A New Kind of Science [citation]