

A057452


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


9



8, 19, 67, 331, 2221, 19577, 219613, 3042161, 50728129, 997525853, 22742734291, 592821132889, 17461204521323, 575411103069067, 21034688742654437, 846729487306354343
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OFFSET

1,1


COMMENTS

Lubomir Alexandrov informs me that he studied this sequence in his 1965 notebook.  N. J. A. Sloane, May 23 2008
a(n) = the Matula number of the rooted tree Q(n) obtained by attaching 3 pendant edges at one of the endpoints of the pathtree P(n) (on n vertices); the root is the other endpoint.  Emeric Deutsch, Jan 18 2014


LINKS

Table of n, a(n) for n=1..16.
Lubomir Alexandrov, Prime Number Sequences And Matrices Generated By Counting Arithmetic Functions, Communications of the Joint Institute of Nuclear Research, E5200255, Dubna, 2002.
E. Deutsch, Tree statistics from Matula numbers, arXiv preprint arXiv:1111.4288 [math.CO], 2011.
E. Deutsch, Rooted tree statistics from Matula numbers, Discrete Appl. Math., 160, 2012, 23142322.
F. Goebel, On a 11correspondence between rooted trees and natural numbers, J. Combin. Theory, B 29 (1980), 141143.
I. Gutman and A. Ivic, On Matula numbers, Discrete Math., 150, 1996, 131142.
I. Gutman and YeongNan Yeh, Deducing properties of trees from their Matula numbers, Publ. Inst. Math., 53 (67), 1993, 1722.
D. Matula, A natural rooted tree enumeration by prime factorization, SIAM Rev. 10 (1968) 273.


MAPLE

a := proc (n) option remember: if n = 1 then 8 else ithprime(a(n1)) end if end proc: seq(a(n), n = 1 .. 9); # Emeric Deutsch, Jan 18 2014


MATHEMATICA

NestList[ Prime, 8, 12 ]


CROSSREFS

Cf. A007097, A235120. Apart from initial terms, probably same as A005518.
Sequence in context: A278947 A153026 A297302 * A091560 A061877 A297459
Adjacent sequences: A057449 A057450 A057451 * A057453 A057454 A057455


KEYWORD

nonn,hard,more


AUTHOR

Robert G. Wilson v, Sep 26 2000


EXTENSIONS

More references and links from Emeric Deutsch, Jan 18 2014
a(14)a(16) from Robert G. Wilson v, Mar 07 2017 using Kim Walisch's primecount


STATUS

approved



