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Search: id:A005596
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| A005596 |
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Decimal expansion of Artin's constant product(1-1/(p^2-p), p=prime).
(Formerly M2608)
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+0
19
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| 3, 7, 3, 9, 5, 5, 8, 1, 3, 6, 1, 9, 2, 0, 2, 2, 8, 8, 0, 5, 4, 7, 2, 8, 0, 5, 4, 3, 4, 6, 4, 1, 6, 4, 1, 5, 1, 1, 1, 6, 2, 9, 2, 4, 8, 6, 0, 6, 1, 5, 0, 0, 4, 2, 0, 9, 4, 7, 4, 2, 8, 0, 2, 4, 1, 7, 3, 5, 0, 1, 8, 2, 0, 4, 0, 0, 2, 8, 0, 8, 2, 3, 4, 4, 3, 0, 4, 3, 1, 7, 0, 8, 7, 2, 5, 0, 5, 6
(list; cons; graph; listen)
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OFFSET
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0,1
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. W. Wrench, Jr., Evaluation of Artin's constant and the twin-prime constant, Math. Comp., 15 (1961), 396-398.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,1000
G. Niklasch, Some number theoretical constants: 1000-digit values
G. Niklasch, Artin's constant
S. Plouffe, The Artin's Constant=product(1-1/p**2-p), p=prime)
T. O. Silva, Plouffe's Inverter, The first 500 digits of Artin's constant
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics
Eric Weisstein's World of Mathematics, Full Reptend Prime
Index entries for sequences related to Artin's conjecture
Pieter Moree, Artin's primitive root conjecture - a survey, math.NT/0412262
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FORMULA
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Equals product_{j=2..infinity} 1/Zeta(j)^A006206(j), where Zeta(.)=A013661, A002117 etc. is Riemann's zeta function. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 14 2009]
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EXAMPLE
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0.37395581361920228805472805434641641511162924860615...
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PROGRAM
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Contribution from Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 15 2009: (Start)
(PARI) { default(realprecision, 1002); artin=\
0.37395581361920228805472805434641641511162924860615004209474280241\
7350182040028082344304317087250568981603906684726306892164063898810\
2172488214240511648074688474732446190316098375630506508175207397645\
8876161134610488557710895423001568593930861519821929642278412653212\
5244466355213639166532148577760847770575614106561790747673010180152\
3834700979012941585934497045575775038261284118716994281028142115314\
2036264703556131331947295631469607736716406952926852216413988130891\
9849653905380283513984198532153783661009992969375741288698893807079\
2344830973486210808921921878270276889967089069326398137400176788725\
5208161085359328734788241648239623954848113039227397597864113180807\
5284312680251949287748937850433208186901363098622293262348364966537\
9584657923892328366673001212172126824119215427225308878008335267195\
1982335057403019303630767771830606746868867991878737057085632141350\
1889973479946121120834579501172965785460587371707657249964547353679\
884468141886104542087846835994670548028055671229800106121823971926; x=10*artin; for (n=0, 1000, d=floor(x); x=(x-d)*10; write("b005596.txt", n, " ", d)); } (End)
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CROSSREFS
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Cf. A048296, A065414, A001913, A001122.
Sequence in context: A131917 A019785 A074176 this_sequence A159566 A096385 A088837
Adjacent sequences: A005593 A005594 A005595 this_sequence A005597 A005598 A005599
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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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EXTENSIONS
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More terms from Tom\'as Oliveira e Silva (http://www.ieeta.pt/~tos)
Fixed my PARI program, had -n Harry J. Smith (hjsmithh(AT)sbcglobal.net), May 19 2009
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