A343981 a(n) is the least integer h such that there exists a Pythagorean triple whose hypotenuse is h and whose other legs z satisfy A176774(z) = n.

35, 0, 13, 0, 2727, 104, 13911, 17370, 426996, 1855, 340119, 89375, 3588, 37400, 3034, 57709, 2103750, 88400, 53290, 506817, 15263560, 141921, 660350, 3372270, 419356, 40716, 57526469, 356025, 639135, 5316785, 872934, 1493219, 11939849, 119616, 331290, 3008185

Offset: 3

Author

Michel Marcus, May 06 2021

Keywords

• nonn

Comments

a(4)=0 is conjectured.

a(6)=0 because all hexagonal numbers are triangular numbers (see A176948).

Examples

			a(3)=35 because of [21, 28, 35] where A176774(21) = A176774(35) = 3.
a(5)=13 because of [5, 12, 13] where A176774(5) = A176774(12) = 5.
a(7)=2727 because of [540, 2673, 2727] where A176774(540) = A176774(2673) = 7.
		

Links

• Michel Marcus, Table of n, a(n) for n = 3..70
• Michel Marcus, Triples for n = 3..70

Crossrefs

Cf. A176774, A176948.

Programs

PARI

p(s, n) = ((s-2)*n^2 - (s-4)*n)/2;
lista(nn, n) = {my(v = vector(nn, k, p(n, k))); v = select(x->(tp(x)==n), v); my(kh = oo, kv = oo); for (i=1, #v, for (j=1, i, my(h2 = v[i]^2 + v[j]^2, h); if (issquare(h2, &h), if (h < kh, kh = h; kv = [v[j], v[i], kh]);););); kh;}
a(n) = {if (n==4, return (0)); if (n==6, return (0)); my(nn = 2); while ((res=lista(nn, n)) == oo, nn *= 2); res;}