A057452 Prime recurrence: a(1)=8, a(n+1) = a(n)-th prime.

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

Offset: 1

Author

Robert G. Wilson v, Sep 26 2000

Keywords

• nonn
• hard
• more

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 path-tree P(n) (on n vertices); the root is the other endpoint. - Emeric Deutsch, Jan 18 2014

Links

• 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.
• 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, 2314-2322.
• F. Goebel, On a 1-1-correspondence between rooted trees and natural numbers, J. Combin. Theory, B 29 (1980), 141-143.
• I. Gutman and A. Ivic, On Matula numbers, Discrete Math., 150, 1996, 131-142.
• I. Gutman and Yeong-Nan Yeh, Deducing properties of trees from their Matula numbers, Publ. Inst. Math., 53 (67), 1993, 17-22.
• D. Matula, A natural rooted tree enumeration by prime factorization, SIAM Rev. 10 (1968) 273.

Crossrefs

Cf. A007097, A235120. Apart from initial terms, probably same as A005518.

Programs

Maple

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

Mathematica

NestList[ Prime, 8, 12 ]

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