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 A239487 Maximum number of diameters of an indecomposable algebraic curve of degree n. 0
 3, 6, 5, 12, 7, 18, 9, 12, 11, 30, 13, 16, 15, 18, 17, 20, 19, 30, 21, 24, 23, 30, 25, 28, 27, 30, 29, 32, 31, 34, 33, 36, 35, 38, 37, 40, 39, 42, 41, 44, 43, 46, 45, 48, 47, 50, 49, 52, 51, 54, 53, 56, 55, 58, 57, 60, 59, 62, 61, 64, 63, 66, 65, 68, 67, 70 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 REFERENCES F. Le Lionnais, Les Nombres Remarquables. Paris: Hermann, p. 70, 1983 (apparently there is an error concerning the list of exceptions: Le Lionnais has 10, 12, 24, whereas both Lebesgue papers say 12, 20, 24). LINKS Henri Lebesgue, Sur les diamètres rectilignes des courbes algébriques planes, Bulletin de la Société Mathématique de France, 49 (1921), pp. 109-150. Henri Lebesgue, Les Coniques, Préface de M. Paul Montel, Paris, Gauthier-Villars, 1942 FORMULA a(n) = n if n is odd, a(n) = n + 2 if n is even except for a(6) = 12, a(8) = 18, a(12) = a(20) = a(24) = 30, and a(16) = 18. Empirical g.f.: x^3*(4*x^24 -4*x^23 -4*x^22 +4*x^21 +8*x^20 -8*x^19 -8*x^18 +8*x^17 +16*x^12 -16*x^11 -16*x^10 +16*x^9 +8*x^8 -8*x^7 -4*x^6 +4*x^5 -4*x^4 +4*x^3 -4*x^2 +3*x +3) / ((x -1)^2*(x +1)). - Colin Barker, Sep 23 2014 PROG (PARI) a(n) = if (n % 2, n, if (n == 6, 12, if (n == 8, 18, if ((n==12) ||(n==20) ||(n==24) , 30, if (n==16, 18, n+2))))); CROSSREFS Sequence in context: A007479 A076535 A285327 * A246979 A246980 A095359 Adjacent sequences:  A239484 A239485 A239486 * A239488 A239489 A239490 KEYWORD nonn AUTHOR Michel Marcus, Mar 20 2014 STATUS approved

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Last modified August 10 12:19 EDT 2020. Contains 336379 sequences. (Running on oeis4.)