A005792 Positive numbers that are the sum of 2 squares or 3 times a square. (Formerly M0529)

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

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.

Index entries for sequences related to sums of squares

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

N. J. A. Sloane.

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