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%I M0529 #34 Oct 21 2017 16:06:38
%S 1,2,3,4,5,8,9,10,12,13,16,17,18,20,25,26,27,29,32,34,36,37,40,41,45,
%T 48,49,50,52,53,58,61,64,65,68,72,73,74,75,80,81,82,85,89,90,97,98,
%U 100,101,104,106,108,109,113,116,117,121,122,125,128,130,136,137,144,145
%N Positive numbers that are the sum of 2 squares or 3 times a square.
%C Equivalently, numbers of the form k^2, k^2+m^2, or 3*k^2, where k >= 1, m >= 1.
%C Theorem (Golomb; Snover et al.): A triangle can be partitioned into n pairwise congruent triangles iff n is of the form k^2, k^2+m^2, or 3*k^2.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A. Soifer, How Does One Cut A Triangle?, Chapter 2, CEME, Colorado Springs CO 1990.
%H Rémy Sigrist, <a href="/A005792/b005792.txt">Table of n, a(n) for n = 1..10000</a>
%H Solomon W. Golomb, <a href="http://www.jstor.org/stable/3611700">Replicating figures in the plane</a>, The mathematical gazette 48.366 (1964): 403-412.
%H Murray Klamkin, <a href="/A074764/a074764.pdf">Review of "How Does One Cut a Triangle?" by Alexander Soifer</a>, Amer. Math. Monthly, October 1991, pp. 775-. [Annotated scanned copy of pages 775-777 only] See "Grand Problem 1".
%H S. Snover, <a href="/A005789/a005789.pdf">Letter to N. J. A. Sloane, May 1991</a>
%H S. L. Snover, C. Wavereis and J. K. Williams, <a href="https://doi.org/10.1016/0012-365X(91)90110-N">Rep-tiling for triangles</a>, Discrete Math. 91 (1991), no. 2, 193-200.
%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>
%Y Union of positive terms of A000290, A000404, A033428.
%Y Cf. A074764.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_.
%E More terms from Larry Reeves (larryr(AT)acm.org), Mar 21 2001
%E Entry revised by _N. J. A. Sloane_, Nov 30 2016
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