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Pickover's Sequence


Pickover's sequence gives the first starting positions in the decimal expansion of pi, excluding the leading 3, at which the first n digits of e occur, for each positive integer n. The matched digits include the leading 2 of e and omit its decimal point, and positions are counted from the first fractional digit of pi as position 1. 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, the sequence of first starting positions in the decimal expansion of e, excluding the leading 2, at which the first n digits of pi occur is obtained by including the leading 3 of pi and omitting its decimal point. Positions are counted from the first fractional digit of e as position 1. 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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References

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

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Pickover's Sequence

Cite this as:

Weisstein, Eric W. "Pickover's Sequence." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PickoversSequence.html

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