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Search: id:A007097
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| A007097 |
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Primeth recurrence: a(n+1) = a(n)-th prime. (Formerly M0734)
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+0 63
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| 1, 2, 3, 5, 11, 31, 127, 709, 5381, 52711, 648391, 9737333, 174440041, 3657500101, 88362852307, 2428095424619, 75063692618249, 2586559730396077, 98552043847093519, 4123221751654370051
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A007097(n) = Min {k : A109301(k) = n} = the first k whose rote height is n, the level set leader or minimum inverse function corresponding to A109301. - Jon Awbrey (jawbrey(AT)att.net), Jun 26 2005
Lubomir Alexandrov (alexandr(AT)theor.jinr.ru) informs me that he studied this sequence in his 1965 notebook. - njas, May 23 2008.
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REFERENCES
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Lubomir Alexandrov, unpublished notes, circa 1960.
Lubomir Alexandrov, "On the nonasymptotic prime number distribution", LANL.math.NT/9811096, Los Alamos, 1998
Lubomir Alexandrov,"The Eratosthenes Progression p(k+1)=p(p(k)), k=0,1,2,..., p(0)=1,4,6,... Determines an Inner Prime Number Distribution Law", Second Int. Conf. "Modern Trends in Computational Physics", Jul 24-29, 2000, Dubna, Russia, Book of Abstracts, p. 19.
L. Longeri, Towards understanding nature and the aesthetics of prime numbers, https://www.longeri.org/prime/nature.html
Lubomir Alexandrov, "Prime Number Sequences And Matrices Generated By Counting Arithmetic Functions", Communications of the Joint Institute of Nuclear Research, E5-2002-55, Dubna, 2002.
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LINKS
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M. Deleglise, Computation of large values of pi(x)
N. Fernandez, An order of primeness, F(p)
N. J. A. Sloane, My favorite integer sequences, in Sequences and their Applications (Proceedings of SETA '98).
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MATHEMATICA
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NestList[Prime@# &, 1, 16] (from Robert G. Wilson v (rgwv(at)rgwv.com), May 30 2006)
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CROSSREFS
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Cf. A000720, A049076-A049081.
Cf. A109301.
Sequence in context: A090709 A112279 A130166 this_sequence A132745 A124538 A124627
Adjacent sequences: A007094 A007095 A007096 this_sequence A007098 A007099 A007100
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KEYWORD
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nonn,hard,nice
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AUTHOR
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njas, Robert G. Wilson v (rgwv(AT)rgwv.com).
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EXTENSIONS
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15th term corrected and 2 more terms added by loria.fr!Paul.Zimmermann (Paul Zimmermann).
a(18) and a(19) from David Baugh (dbaugh(AT)rice.edu), Oct 25 2007
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