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A007097
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Primeth recurrence: a(n+1) = a(n)-th prime.
(Formerly M0734)
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74
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1, 2, 3, 5, 11, 31, 127, 709, 5381, 52711, 648391, 9737333, 174440041, 3657500101, 88362852307, 2428095424619, 75063692618249, 2586559730396077, 98552043847093519, 4123221751654370051, 188272405179937051081, 9332039515881088707361
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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. - N. J. A. Sloane (njas(AT)research.att.com), May 23 2008.
a(n) is the Matula-Goebel number of the rooted path tree on n+1 vertices. The Matula-Goebel number of a rooted tree can be defined in the following recursive manner: to the one-vertex tree there corresponds the number 1; to a tree T with root degree 1 there corresponds the t-th prime number, where t is the Matula-Goebel number of the tree obtained from T by deleting the edge emanating from the root; to a tree T with root degree m>=2 there corresponds the product of the Matula-Goebel numbers of the m branches of T. [Emeric Deutsch, February 18, 2012]
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REFERENCES
| Lubomir Alexandrov, unpublished notes, circa 1960.
Lubomir Alexandrov, "On the nonasymptotic prime number distribution", LANL.math.NT/9811096, Los Alamos, 1998
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.
Lubomir Alexandrov,"The Eratosthenes Progression p(k+1)=pi^{-1}(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. Available at arXiv:math/0105154.
L. Longeri, Towards understanding nature and the aesthetics of prime numbers, https://www.longeri.org/prime/nature.html
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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
| NestList[Prime@# &, 1, 16] (from Robert G. Wilson v (rgwv(at)rgwv.com), May 30 2006)
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PROG
| (PARI) print1(p=1); until(, print1(", "p=prime(p))) \\ - M. F. Hasler, Oct 09 2011
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CROSSREFS
| Cf. A000720, A049076-A049081, A109301, A131842.
Sequence in context: A090709 A112279 A130166 * A173422 A132745 A124538
Adjacent sequences: A007094 A007095 A007096 * A007098 A007099 A007100
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KEYWORD
| nonn,hard,nice,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com).
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EXTENSIONS
| 15th term corrected and 2 more terms added by loria.fr!Paul.Zimmermann (Paul Zimmermann).
a(18) and a(19) found by David Baugh using a program by Xavier Gourdon and Andrey V. Kulsha, Oct 25 2007
a(20) and a(21) found by Andrey V. Kulsha using a program by Xavier Gourdon, Oct 02 2011
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