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

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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.

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Mar 21 2001

Entry revised by N. J. A. Sloane, Nov 30 2016