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Search: id:A019727
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| A019727 |
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Decimal expansion of sqrt(2*Pi). |
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+0
3
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| 2, 5, 0, 6, 6, 2, 8, 2, 7, 4, 6, 3, 1, 0, 0, 0, 5, 0, 2, 4, 1, 5, 7, 6, 5, 2, 8, 4, 8, 1, 1, 0, 4, 5, 2, 5, 3, 0, 0, 6, 9, 8, 6, 7, 4, 0, 6, 0, 9, 9, 3, 8, 3, 1, 6, 6, 2, 9, 9, 2, 3, 5, 7, 6, 3, 4, 2, 2, 9, 3, 6, 5, 4, 6, 0, 7, 8, 4, 1, 9, 7, 4, 9, 4, 6, 5, 9, 5, 8, 3, 8, 3, 7, 8, 0, 5, 7, 2, 6
(list; cons; graph; listen)
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OFFSET
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1,1
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COMMENT
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Pickover says that the expression: lim(n=1,infinity) e^n(n!) / n^n * sqrt(n) = sqrt(2*Pi) is beautiful because it connects Pi, e, radicals, factorials and infinite limits. - Jason Earls (zevi_35711(AT)yahoo.com), Mar 16 2001
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REFERENCES
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C. Pickover, Wonders of Numbers, Oxford University Press, NY, 2001, p. 307.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,20000
C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review
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FORMULA
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Equal to lim(n=1, infinity)e^n*(n!)/n^n*sqrt(n).
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EXAMPLE
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2.506628274631000502415765284811045253006986740609938316629923576342293... [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 31 2009]
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PROGRAM
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(PARI) { default(realprecision, 20080); x=sqrt(2*Pi); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b019727.txt", n, " ", d)); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 31 2009]
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CROSSREFS
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Cf. A058293 Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 31 2009]
Sequence in context: A058204 A090625 A021403 this_sequence A011184 A157214 A066033
Adjacent sequences: A019724 A019725 A019726 this_sequence A019728 A019729 A019730
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KEYWORD
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nonn,cons
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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