A185223 A185128(n) is the a(n)-th triangular number.

6, 18, 37, 44, 86, 91, 116, 132, 247, 278, 392, 613, 637, 662, 798, 847, 912, 1164, 1235, 1362, 1430, 1638, 1735, 1991, 2056, 2090, 2167, 2364, 2537, 2736, 3139, 3478, 3751, 3867, 4298, 4422, 4553, 5202, 6068, 6391, 6500, 7241, 7859, 7957, 8378, 9309, 9793

Offset: 1

Author

Martin Renner, Jan 20 2012

Keywords

• nonn

Comments

Side lengths where both triangular numbers are the same (A053141) are not included. - R. J. Mathar, Feb 11 2018

See A185128 for further information.

Examples

			A185128(2) = 171 which is the 18th triangular number, so a(2) = 18.
		

References

• Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966, p. 197, no. 8.

Links

• R. J. Mathar, Table of n, a(n) for n = 1..58
• N. J. A. Sloane, Annotated scan of Beiler's Table 81, based on page 197 of Beiler's "Recreations in the Theory of Numbers: The Queen of Mathematics Entertains", New York, Dover, First ed., 1964.

Crossrefs

Cf. A000217, A185128, A185129, A185233, A185243, A185253, A185257, A185258.

Programs

PARI

lista(nn) = {v = vector(nn, n, n*(n+1)/2); for (n=2, nn, for (k=1, n-1, if (ispolygonal(v[n]+v[k], 3) && ispolygonal(v[n]-v[k], 3), print1(n, ", "));););} \\ Michel Marcus, Jan 08 2015

Extensions

Edited (with a simpler definition) by N. J. A. Sloane, Dec 28 2024