Search: id:A064648
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%I A064648
%S A064648 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,
%T A064648 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,
%U A064648 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
%N A064648 Decimal expansion of sum of reciprocals of primorial numbers: (1/2)+(1/
               6)+(1/30)+(1/210)+.... = 0.7052301717918009651474316828882485137435776391...
%C A064648 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
%D A064648 Engel, F. "Entwicklung der Zahlen nach Stammbruechen" Verhandlungen der 
               52. Versammlung deutscher Philologen und Schulmaenner in Marburg. 
               pp. 190-191, 1913.
%H A064648 Harry J. Smith, <a href="b064648.txt">Table of n, a(n) for n=0,...,20000</
               a>
%H A064648 S. Plouffe, <a href="http://pi.lacim.uqam.ca/piDATA/primeprod.txt">Sum 
               of the product of prime reciprocals</a>
%H A064648 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               EngelExpansion.html">Engel Expansion.</a>
%e A064648 0.705230171791800965147431682888248513743577639109154328192267913813919... 
               [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 21 2009]
%t A064648 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)
%o A064648 (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]
%Y A064648 Cf. A002110.
%Y A064648 Cf. A054543, A000027, A053977, A006784, A028259.
%Y A064648 Cf. A165509 Continued fraction. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), 
               Sep 21 2009]
%Y A064648 Sequence in context: A021997 A099737 A033150 this_sequence A116198 A137915 
               A130203
%Y A064648 Adjacent sequences: A064645 A064646 A064647 this_sequence A064649 A064650 
               A064651
%K A064648 cons,nonn
%O A064648 0,1
%A A064648 Labos E. (labos(AT)ana.sote.hu), Oct 04 2001

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