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 A005792 Positive numbers that are the sum of 2 squares or 3 times a square. (Formerly M0529) 2
 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, 48, 49, 50, 52, 53, 58, 61, 64, 65, 68, 72, 73, 74, 75, 80, 81, 82, 85, 89, 90, 97, 98, 100, 101, 104, 106, 108, 109, 113, 116, 117, 121, 122, 125, 128, 130, 136, 137, 144, 145 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equivalently, numbers of the form k^2, k^2+m^2, or 3*k^2, where k >= 1, m >= 1. 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. REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). A. Soifer, How Does One Cut A Triangle?, Chapter 2, CEME, Colorado Springs CO 1990. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 Solomon W. Golomb, Replicating figures in the plane, The mathematical gazette 48.366 (1964): 403-412. Murray Klamkin, Review of "How Does One Cut a Triangle?" by Alexander Soifer, Amer. Math. Monthly, October 1991, pp. 775-. [Annotated scanned copy of pages 775-777 only] See "Grand Problem 1". S. Snover, Letter to N. J. A. Sloane, May 1991 S. L. Snover, C. Wavereis and J. K. Williams, Rep-tiling for triangles, Discrete Math. 91 (1991), no. 2, 193-200. CROSSREFS Union of positive terms of A000290, A000404, A033428. Cf. A074764. Sequence in context: A023760 A032901 A260113 * A270430 A318932 A259185 Adjacent sequences:  A005789 A005790 A005791 * A005793 A005794 A005795 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Larry Reeves (larryr(AT)acm.org), Mar 21 2001 Entry revised by N. J. A. Sloane, Nov 30 2016 STATUS approved

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Last modified December 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)