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 A000934 Chromatic number (or Heawood number) Chi(n) of surface of genus n. (Formerly M3292 N1327) 8
 4, 7, 8, 9, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 16, 17, 17, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 27, 27, 27, 27, 28, 28, 28, 28, 28, 29, 29, 29, 29, 30, 30, 30, 30, 31, 31, 31, 31, 31, 32, 32 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(0) = 4 is the celebrated four-color theorem. "In 1890 P. Heawood discovered the formula ... and proved that the number of colors required to color a map on an n-holed torus (n >= 1) is at most Chi(n). In 1968 G. Ringel and J. W. T. Youngs succeeded in showing that for every n>=1, there is a configuration of Chi(n) countries on an n-holed torus such that each country shares a border with each of the Chi(n)-1 other countries; this shows that Chi(n) colors may be necessary. This completed the proof that Heawood's formula is indeed the correct chromatic number function for the n-holed torus." ... "Heawood's formula is in fact valid for n = 0." - Stan Wagon REFERENCES K. Appel and W. Haken, Every planar map is four colorable. With the collaboration of J. Koch. Contemporary Mathematics, 98. American Mathematical Society, Providence, RI, 1989. xvi+741 pp. ISBN: 0-8218-5103-9. K. Appel and W. Haken, "The Four-Color Problem" in Mathematics Today (L. A. Steen editor), Springer NY 1978. K. Appel and W. Haken, "The Solution of the Four-Color Map Problem", Scientific American vol. 237 no.4 pp. 108-121 1977. D. Barnett, Map coloring, Polyhedra and The Four-Color Problem, Dolciani Math. Expositions No. 8, Math. Asso. of Amer., Washington DC 1984. J. H. Cadwell, Topics in Recreational Mathematics, Chapter 8 pp. 76-87 Cambridge Univ. Press 1966. K. J. Devlin, All The Math That's Fit To Print, Chap. 17; 67 pp. 46-8; 161-2 MAA Washington DC 1994. K. J. Devlin, Mathematics: The New Golden Age, Chapter 7, Columbia Univ. Press NY 1999. M. Gardner, New Mathematical Diversions, Chapter 10 pp. 113-123, Math. Assoc. of Amer. Washington DC 1995. J. L. Gross and T. W. Tucker, Topological Graph Theory, Wiley, 1987; see Table 5.1 p. 221. M. E. Lines, Think of a Number, Chapter 10 pp. 91-100 Institute of Physics Pub. London 1990. Robertson, N.; Sanders, D. P.; Seymour, P. and Thomas, R., A new proof of the four-color theorem. Electron. Res. Announc. Amer. Math. Soc. 2 (1996), no. 1, 17-25. W. W. Rouse Ball & H. S. M. Coxeter, Mathematical Recreations and Essays, Chapter VIII pp. 222-242 Dover NY 1987. W. L. Schaaf, Recreational Mathematics. A guide to the literature, Chapter 4.7 pp. 74-6 NCTM Washington DC 1963. W. L. Schaaf, A Bibliography of Recreational Mathematics Vol. 2, Chapter 4.6 pp. 75-9 NCTM Washington DC 1972. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). I. Stewart, From Here to Infinity, Chapter 8 pp. 104-112, Oxford Univ.Press 1996. H. Tietze, Famous Problems of Mathematics, Chapter XI pp. 226-242 Graylock Press Baltimore MD 1966. Stan Wagon, Mathematica In Action, W.H. Freeman and Company, NY, 1991, pages 232 - 237. R. Wilson, Four Colors Suffice, Princeton Univ. Press, 2002. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe) P. Alfeld, The Four Color Map Problem K. Appel and W. Haken, Every planar map is four colorable. I. Discharging, Illinois J. Math. 21 (1977), no. 3, 429-490. K. Appel and W. Haken, Every planar map is four colorable. II. Reducibility. Illinois J. Math. 21 (1977), 491-567. K. Appel and W. Haken, The Four-Color proof suffices, Mathematical Intelligencer 8 no.1 pp. 10-20 1986. P. DÃ¶rre, Every planar map is 4-color and 5-choosable, arXiv:math/0408384 [math.GM], 2004-2013. R. K. Guy, Letters to N. J. A. Sloane, June-August 1968 R. E. Kenyon, Jr., Toward an Inductive Solution for the Four Color Problem C. Lozier, The Four Color Theorem MegaMath, Four Color Theorem J. J. O'Connor & E. F. Robertson, The four color theorem G. Ringel & J. W. T. Youngs, Solution Of The Heawood Map-Coloring Problem, Proc. Nat. Acad. Sci. USA, 60 (1968), 438-445. N. Robertson et al., The Four Color Theorem N. Robertson, D. Sanders, P. Seymour and R. Thomas, The four-color theorem, J. Combin. Theory Ser. B 70 (1997), no. 1, 2-44. D. S. Silver, Map Quest : Review of "Four Colors Suffice" by R.Wilson Eric Weisstein's World of Mathematics, Chromatic Number Eric Weisstein's World of Mathematics, Heawood Conjecture Eric Weisstein's World of Mathematics, Torus Coloring FORMULA a(n) = floor( (7+sqrt(1+48n))/2 ). MAPLE A000934 := n-> floor((7+sqrt(1+48*n))/2); MATHEMATICA Table[ Floor[ N[(7 + Sqrt[48n + 1])/2] ], {n, 0, 100} ] PROG (Haskell) a000934 = floor . (/ 2) . (+ 7) . sqrt . (+ 1) . (* 48) . fromInteger -- Reinhard Zumkeller, Dec 03 2012 (MAGMA) [Floor((7+Sqrt(1+48*n))/2): n in [0..70]]; // Vincenzo Librandi, Jul 09 2017 CROSSREFS Cf. A000703, A006343. Sequence in context: A310936 A082390 A011517 * A180692 A004710 A060257 Adjacent sequences:  A000931 A000932 A000933 * A000935 A000936 A000937 KEYWORD easy,nice,nonn AUTHOR EXTENSIONS More terms from Robert G. Wilson v, Dec 08 2000 STATUS approved

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Last modified October 23 11:19 EDT 2019. Contains 328345 sequences. (Running on oeis4.)