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 A336753 Largest side of integer-sided triangles whose sides a < b < c are in arithmetic progression. 5
 4, 5, 7, 6, 8, 7, 10, 9, 8, 11, 10, 9, 13, 12, 11, 10, 14, 13, 12, 11, 16, 15, 14, 13, 12, 17, 16, 15, 14, 13, 19, 18, 17, 16, 15, 14, 20, 19, 18, 17, 16, 15, 22, 21, 20, 19, 18, 17, 16, 23, 22, 21, 20, 19, 18, 17, 25, 24, 23, 22, 21, 20, 19, 18, 26, 25, 24, 23, 22, 21, 20, 19 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The triples of sides (a,b,c) with a < b < c are in increasing order of perimeter = 3*b, and if perimeters coincide, then by increasing order of the smallest side. This sequence lists the c's. Equivalently: largest side of integer-sided triangles such that b = (a+c)/2 with a < c. c >= 4 and each largest side c appears floor((c-1)/3) = A002264(c-1) times but not consecutively. For each c = 5*k, k>=1, there exists exactly one right triangle (3*k, 4*k, 5*k) whose sides a < b < c are in arithmetic progression. For the corresponding primitive triples and miscellaneous properties and references, see A336750. REFERENCES V. Lespinard & R. Pernet, Trigonométrie, Classe de Mathématiques élémentaires, programme 1962, problème B-290 p. 121, André Desvigne. LINKS FORMULA a(n) = A336750(n, 3). EXAMPLE c = 4 only for the smallest triangle (2, 3, 4). c = 5 only for Pythagorean triple (3, 4, 5). c = 6 only for triple (4, 5, 6). c = 7 for the two triples (3, 5, 7) and (5, 6, 7). MAPLE for b from 3 to 30 do for a from b-floor((b-1)/2) to b-1 do c := 2*b - a; print(c); end do; end do; CROSSREFS Cf. A336750 (triples), A336751 (smallest side), A307136 (middle side), this sequence (largest side), A336754 (perimeter). Cf. A335896 (largest side when triangles angles are in arithmetic progression). Sequence in context: A016720 A104140 A003563 * A023833 A151551 A021690 Adjacent sequences:  A336750 A336751 A336752 * A336754 A336755 A336756 KEYWORD nonn AUTHOR Bernard Schott, Aug 25 2020 STATUS approved

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Last modified August 6 00:46 EDT 2021. Contains 346493 sequences. (Running on oeis4.)