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A229461 Numbers n such that there is no convex pentagon that can be decomposed into n pairwise congruent regular equilateral triangles. 3
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 16, 18, 21, 22, 24, 25, 30, 33, 37, 40, 42, 45, 48, 57, 58, 70, 72, 78, 85, 88, 93, 102, 105, 120, 130, 133, 165, 168, 177, 190, 210, 232, 253, 273, 280, 312, 330, 345, 357, 385, 408, 462, 520, 760, 840, 1320, 1365, 1848 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture: These 59 numbers are all such exceptions.

Terms are idoneal numbers (A000926) except for the six terms of A229462.

Numbers k not expressible as k = x^2 - y^2 - z^2 with x,y,z >= 1 and x > y+z.

LINKS

Table of n, a(n) for n=1..59.

Eike Hertel, Reguläre Dreieckspflasterungen konvexer Polygone, Jenaer Schriften zur Mathematik und Informatik, Math/Inf/01/13, 2013 (preprint).

Eike Hertel, Christian Richter, Tiling Convex Polygons with Congruent Equilateral Triangles, Discrete Comput Geom (2014) 51:753-759.

E. Kani, Idoneal numbers and some generalizations, Ann Sci. Math. Québec, 35 (2011), pp. 197-227.

Kival Ngaokrajang, Illustration of initial terms

CROSSREFS

Cf. A000926 (idoneal numbers), A229462 (idoneal numbers not in this sequence), A229757 (hexagon exception numbers), A025052 (numbers not of form a*b+b*c+c*a).

Sequence in context: A228897 A068095 A064390 * A230709 A080671 A286608

Adjacent sequences:  A229458 A229459 A229460 * A229462 A229463 A229464

KEYWORD

nonn

AUTHOR

Suggested by Eike Hertel, Hugo Pfoertner, Sep 24 2013

STATUS

approved

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Last modified October 15 17:24 EDT 2019. Contains 328037 sequences. (Running on oeis4.)