The earliest known mention of this idea occurs in Douglas Hofstadter's 1985 book Metamagical Themas, where Hofstadter states[3][4] I myself once learned 380 digits of π, when I was a crazy high-school kid.
My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes "999999", so that I could recite it out loud, come to those six 9s, and then impishly say, "and so on!
For a normal number sampled uniformly at random, the probability of a specific sequence of six digits occurring this early in the decimal representation is about 0.08%.
The next sequence of six consecutive identical digits is again composed of 9s, starting at position 193,034.
[7] The positions of the first occurrence of a string of 1, 2, 3, 4, 5, 6, 7, 8, and 9 consecutive 9s in the decimal expansion are 5; 44; 762; 762; 762; 762; 1,722,776; 36,356,642; and 564,665,206, respectively (sequence A048940 in the OEIS).