A185233 A185129(n) is the a(n)-th triangular number.

5, 14, 27, 39, 65, 54, 104, 125, 242, 209, 374, 459, 350, 275, 714, 782, 350, 1155, 1224, 1022, 1425, 840, 594, 1715, 1700, 1869, 702, 1260, 1224, 1014, 2645, 2430, 3185, 1127, 4094, 3317, 1274, 5124, 6060, 3834, 3059, 6174, 5565, 7749, 8349, 7395, 7344

Offset: 1

Author

Martin Renner, Jan 20 2012

Keywords

• nonn

Comments

See A185128 for further information.

Examples

			A185122(2) = 105 which is the 14th triangular number, so a(2) = 14.
		

References

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

Links

• 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, A185223, 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(k, ", "));););} \\ Michel Marcus, Jan 08 2015

Extensions

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