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Prime recurrence: a(1)=8, a(n+1) = a(n)-th prime.
10

%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