The Earls sequence gives the starting position in the decimal digits of  (or in general, any constant), not counting digits to the left of the decimal point, at which a string of  copies of the number  first occurs. The following table gives generalized Earls sequences for various constants, including .

Note that the 20-digit sequence  does not occur in the first  digits of , nor in fact do any of the -digit sequences  for any two-digit number  with  and  (E. W. Weisstein, Jul. 20, 2013).

REFERENCES:

Anderson, D. "The Pi-Search Page." http://www.angio.net/pi/piquery.

Pickover, C. A. The Mathematics of Oz: Mental Gymnastics from Beyond the Edge. New York: Cambridge University Press, p. 338, 2002.

Sloane, N. J. A. Sequences A061073, A224819, A224826, A224828, A224836, A224844, A224871, A224874, A224896, A224897, A225242, A225763, A228242, A228243, A229074, and A229071 in "The On-Line Encyclopedia of Integer Sequences."