A380875 Indices of triangular numbers (A000217) which are also perimeters of integer-sided right triangles (A010814).

8, 15, 20, 23, 24, 27, 32, 35, 39, 44, 47, 48, 51, 55, 56, 59, 60, 63, 64, 68, 71, 72, 75, 76, 79, 80, 84, 87, 91, 92, 95, 96, 99, 104, 111, 112, 115, 116, 119, 120, 123, 124, 128, 132, 135, 139, 140, 143, 144, 147, 152, 155, 159, 160, 164, 167, 168, 171, 175, 176, 179, 180, 183, 184, 187, 188

Offset: 1

Author

M. F. Hasler, Mar 20 2025

Keywords

• nonn

Comments

This is relevant for considering integer-sided right triangles whose sides are made of sticks of length 1, 2, 3, ..., n, using all those.

Sequence A382268 considers the special case where these sticks must be used in order.

Links

• Daniel Mondot, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217 (triangular numbers), A010814 (perimeters of right triangles), A382268 (subsequence of k for which a right triangle can be made with linked rods of length 1, ..., k).

Programs

PARI

select( {is_A380875(n)=is_A010814(n*(n+1)\2)}, [1..222])