Pickover's Sequence

Pickover's sequence gives the starting positions in the decimal expansion of pi (ignoring the leading 3) in which the first n digits of e occur (counting the leading 2). So, since pi=3.141592653..., the first digit "2" of e occurs at position 6. Continuing, the sequence is given by 6, 28, 241, 11706, 28024, 33789, 1526800, 73154827, ... (OEIS A090898).

Conversely, consider the sequence formed by the expansion of e (ignoring the leading 2) in which the first n digits of pi occur (counting the leading 3). So, since e=2.718281828459045235..., the first digit "3" of pi occurs at position 17. Continuing, the sequence is given by 17, 189, 856, 17947, 53238, 1436935, 5000482, ... (OEIS A115234).

See also

e-Prime, Earls Sequence, Pi Digits

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Anderson, D. "The Pi-Search Page.", C. A. "A Connection between pi and e." Ch. 99 in The Mathematics of Oz: Mental Gymnastics from Beyond the Edge. New York: Cambridge University Press, pp. 206-208 and 337-339, 2002.Sloane, N. J. A. Sequences A090898 and A115234 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Pickover's Sequence

Cite this as:

Weisstein, Eric W. "Pickover's Sequence." From MathWorld--A Wolfram Web Resource.

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