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Search: id:A064648
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| A064648 |
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Decimal expansion of sum of reciprocals of primorial numbers: (1/2)+(1/6)+(1/30)+(1/210)+.... = 0.7052301717918009651474316828882485137435776391... |
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+0
7
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| 7, 0, 5, 2, 3, 0, 1, 7, 1, 7, 9, 1, 8, 0, 0, 9, 6, 5, 1, 4, 7, 4, 3, 1, 6, 8, 2, 8, 8, 8, 2, 4, 8, 5, 1, 3, 7, 4, 3, 5, 7, 7, 6, 3, 9, 1, 0, 9, 1, 5, 4, 3, 2, 8, 1, 9, 2, 2, 6, 7, 9, 1, 3, 8, 1, 3, 9, 1, 9, 7, 8, 1, 1, 4, 8, 0, 0, 2, 8, 6, 3, 5, 8, 6, 1, 1, 9, 0, 5, 1, 9, 8, 4, 0, 2, 7, 4, 7, 6, 6, 5, 9, 2, 5, 6
(list; cons; graph; listen)
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OFFSET
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0,1
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COMMENT
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This is the real number whose Engel expansion is precisely the sequence of primes A000040. - Jonathan Vos Post (jvospost3(AT)gmail.com), May 04 2005
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REFERENCES
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Engel, F. "Entwicklung der Zahlen nach Stammbruechen" Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg. pp. 190-191, 1913.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,20000
S. Plouffe, Sum of the product of prime reciprocals
Eric Weisstein's World of Mathematics, Engel Expansion.
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EXAMPLE
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0.705230171791800965147431682888248513743577639109154328192267913813919... [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 21 2009]
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MATHEMATICA
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RealDigits[ Sum[1/Product[ Prime[i], {i, n}], {n, 58}], 10, 111][[1]] (from Robert G. Wilson v (rgwv(at)rgwv.com), Aug 05 2005)
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PROGRAM
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(PARI) { default(realprecision, 20080); p=1; s=x=0; for (k=1, 10^9, p*=prime(k); s+=1.0/p; if (s==x, break); x=s ); x*=10; for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b064648.txt", n, " ", d)) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 21 2009]
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CROSSREFS
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Cf. A002110.
Cf. A054543, A000027, A053977, A006784, A028259.
Cf. A165509 Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 21 2009]
Sequence in context: A021997 A099737 A033150 this_sequence A116198 A137915 A130203
Adjacent sequences: A064645 A064646 A064647 this_sequence A064649 A064650 A064651
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KEYWORD
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cons,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Oct 04 2001
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