# Increasing integer sequences and Goldbach's conjecture

RAIRO - Theoretical Informatics and Applications (2006)

- Volume: 40, Issue: 2, page 107-121
- ISSN: 0988-3754

## Access Full Article

top## Abstract

top## How to cite

topTorelli, Mauro. "Increasing integer sequences and Goldbach's conjecture." RAIRO - Theoretical Informatics and Applications 40.2 (2006): 107-121. <http://eudml.org/doc/249725>.

@article{Torelli2006,

abstract = {
Increasing integer sequences include many instances of interesting
sequences and combinatorial structures, ranging from tournaments to addition
chains, from permutations to sequences having the Goldbach property that any integer greater than 1 can be obtained as the sum of two elements
in the sequence. The paper introduces and compares several of these classes
of sequences, discussing recurrence relations, enumerative problems and
questions concerning shortest sequences.
},

author = {Torelli, Mauro},

journal = {RAIRO - Theoretical Informatics and Applications},

language = {eng},

month = {7},

number = {2},

pages = {107-121},

publisher = {EDP Sciences},

title = {Increasing integer sequences and Goldbach's conjecture},

url = {http://eudml.org/doc/249725},

volume = {40},

year = {2006},

}

TY - JOUR

AU - Torelli, Mauro

TI - Increasing integer sequences and Goldbach's conjecture

JO - RAIRO - Theoretical Informatics and Applications

DA - 2006/7//

PB - EDP Sciences

VL - 40

IS - 2

SP - 107

EP - 121

AB -
Increasing integer sequences include many instances of interesting
sequences and combinatorial structures, ranging from tournaments to addition
chains, from permutations to sequences having the Goldbach property that any integer greater than 1 can be obtained as the sum of two elements
in the sequence. The paper introduces and compares several of these classes
of sequences, discussing recurrence relations, enumerative problems and
questions concerning shortest sequences.

LA - eng

UR - http://eudml.org/doc/249725

ER -

## References

top- P. Capell and T.V. Narayana, On Knock-out Tournaments. Canad. Math. Bull.13 (1970) 105–109. Zbl0225.60006
- L. Carlitz, D.P. Roselle and R.A. Scoville, Some Remarks on Ballot-Type Sequences of Positive Integers. J. Combinatorial Theory, Ser. A 11 (1971) 258–271. Zbl0227.05007
- L. Comtet, Advanced Combinatorics. Reidel, Dordrecht (1974). Zbl0283.05001
- M. Cook and M. Kleber, Tournament sequences and Meeussen sequences. Electron. J. Combin.7 (2000), Research Paper 44, p. 16 (electronic). Zbl0973.11028
- J-M. Deshouillers, H.J.J. te Riele and Y. Saouter, New experimental results concerning the Goldbach conjecture, in Proc. 3rd Int. Symp. on Algorithmic Number Theory. Lect. Notes Comput. Sci.1423 (1998) 204–215. Zbl0957.11044
- P. Dusart, The kth prime is greater than k(lnk + lnlnk - 1) for k ≥ 2. Math. Comp.68 (1999) 411–415. Zbl0913.11039
- H. Edelsbrunner, Algorithms in Combinatorial Geometry. Springer, Berlin (1987). Zbl0634.52001
- P. Erdös and M. Lewin, d-Complete Sequences of Integers. Math. Comp.65 (1996) 837–840. Zbl0866.11017
- P.C. Fishburn and F.S. Roberts, Uniqueness in finite measurement, in Applications of Combinatorics and Graph Theory to the Biological and Social Sciences, edited by F.S. Roberts. Springer, New York (1989) 103–137. Zbl0702.92024
- R.K. Guy, Unsolved Problems in Number Theory. Springer, New York, 2nd ed. (1994). Zbl0805.11001
- D.E. Knuth, The Art of Computer Programming, Vols. 2 and 3. Addison-Wesley, Reading (1997 and 1998). Zbl0895.68055
- J.C. Lagarias, The 3x + 1 problem and its generalizations. American Math. Monthly92 (1985) 3–23. Zbl0566.10007
- W.J. LeVeque, Fundamentals of Number Theory. Addison-Wesley, Reading (1977). Zbl0368.10001
- G. Melfi, On Two Conjectures about Practical Numbers. J. Number Theory56 (1996) 205–210. Zbl0848.11002
- M.B. Nathanson, Additive Number Theory. Springer, New York (1996). Zbl0859.11002
- E. Neuwirth, Computing Tournament Sequence Numbers efficiently with Matrix Techniques. Sém. Lothar. Combin.47 (2002), Article B47h, p. 12 (electronic). Zbl1021.05004
- A.M. Odlyzko, Iterated Absolute Values of Differences of Consecutive Primes. Math. Comp.61 (1993) 373–380. Zbl0781.11037
- D.P. Robbins, The Story of 1, 2, 7, 42, 429, 7436, ... Math. Intellig.13 (1991) 12–19. Zbl0723.05004
- J. Richstein, Verifying the Goldbach Conjecture up to 4 x 1014. Math. Comp.70 (2001) 1745–1749. Zbl0989.11050
- N.J.A. Sloane, The On-Line Encyclopedia of Integer Sequences. World-Wide Web URL URIhttp://www.research.att.com/~njas/sequences/
- N.J.A. Sloane and S. Plouffe, The Encyclopedia of Integer Sequences. Academic Press, New York (1995). Zbl0845.11001

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.