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%I #25 Mar 10 2017 19:42:00
%S 8,19,67,331,2221,19577,219613,3042161,50728129,997525853,22742734291,
%T 592821132889,17461204521323,575411103069067,21034688742654437,
%U 846729487306354343
%N Prime recurrence: a(1)=8, a(n+1) = a(n)-th prime.
%C _Lubomir Alexandrov_ informs me that he studied this sequence in his 1965 notebook. - _N. J. A. Sloane_, May 23 2008
%C a(n) = the Matula number of the rooted tree Q(n) obtained by attaching 3 pendant edges at one of the endpoints of the path-tree P(n) (on n vertices); the root is the other endpoint. - _Emeric Deutsch_, Jan 18 2014
%H Lubomir Alexandrov, <a href="http://www1.jinr.ru/Preprints/2002/055(E5-2002-55).pdf">Prime Number Sequences And Matrices Generated By Counting Arithmetic Functions</a>, Communications of the Joint Institute of Nuclear Research, E5-2002-55, Dubna, 2002.
%H E. Deutsch, <a href="http://arxiv.org/abs/1111.4288">Tree statistics from Matula numbers</a>, arXiv preprint arXiv:1111.4288 [math.CO], 2011.
%H E. Deutsch, <a href="http://dx.doi.org/10.1016/j.dam.2012.05.012">Rooted tree statistics from Matula numbers</a>, Discrete Appl. Math., 160, 2012, 2314-2322.
%H F. Goebel, <a href="http://dx.doi.org/10.1016/0095-8956(80)90049-0">On a 1-1-correspondence between rooted trees and natural numbers</a>, J. Combin. Theory, B 29 (1980), 141-143.
%H I. Gutman and A. Ivic, <a href="http://dx.doi.org/10.1016/0012-365X(95)00182-V">On Matula numbers</a>, Discrete Math., 150, 1996, 131-142.
%H I. Gutman and Yeong-Nan Yeh, <a href="http://www.emis.de/journals/PIMB/067/3.html">Deducing properties of trees from their Matula numbers</a>, Publ. Inst. Math., 53 (67), 1993, 17-22.
%H D. Matula, <a href="http://www.jstor.org/stable/2027327">A natural rooted tree enumeration by prime factorization</a>, SIAM Rev. 10 (1968) 273.
%p a := proc (n) option remember: if n = 1 then 8 else ithprime(a(n-1)) end if end proc: seq(a(n), n = 1 .. 9); # _Emeric Deutsch_, Jan 18 2014
%t NestList[ Prime, 8, 12 ]
%Y Cf. A007097, A235120. Apart from initial terms, probably same as A005518.
%K nonn,hard,more
%O 1,1
%A _Robert G. Wilson v_, Sep 26 2000
%E More references and links from _Emeric Deutsch_, Jan 18 2014
%E a(14)-a(16) from _Robert G. Wilson v_, Mar 07 2017 using Kim Walisch's primecount
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