A343892 Side b of integer-sided primitive triangles (a, b, c) where side a is the harmonic mean of the 2 other sides b and c, i.e., 2/a = 1/b + 1/c with b < a < c.

3, 10, 12, 15, 21, 30, 36, 35, 40, 44, 55, 56, 52, 63, 65, 78, 70, 90, 77, 105, 99, 85, 102, 119, 132, 136, 117, 114, 143, 133, 126, 152, 171, 154, 182, 168, 165, 210, 195, 161, 176, 184, 208, 207, 187, 240, 230, 253, 200, 221, 198, 255, 225, 234, 216, 275, 300, 306, 247, 270

Offset

1,1

Comments

The triples (a, b, c) are displayed in increasing order of side a, and if sides a coincide then in increasing order of the side b.

The sequence is not increasing because a(7) = 36 > a(8) = 35, but, these sides b are listed in increasing order in A020890.

The first term appearing twice is 330 and corresponds to triples (435, 330, 638) and (460, 330, 759), the second one is 462 and corresponds to triples (483, 462, 506) and (532, 462, 627).

For the corresponding primitive triples and miscellaneous properties and references, see A343891.

Links

Table of n, a(n) for n=1..60.

Formula

a(n) = A343891(n, 2).

Example

a(4) = 15, because the fourth triple is (21, 15, 35) with side b = 15, satisfying 1/15 = 2/21 - 1/35 and 31-15 < 21 < 31+15.

Maple

for a from 4 to 200 do
for b from floor(a/2)+1 to a-1 do
c := a*b/(2*b-a);
if c=floor(c) and igcd(a, b, c)=1 and c-b<a then print(b); end if;
end do;
end do;

Crossrefs

Cf. A343891 (triples), A020883 (side a), A343893 (side c), A343894 (perimeter).

Cf. A020890 (sides b ordered).

Sequence in context: A283770 A088338 A020890 * A358892 A358893 A317671

Adjacent sequences: A343889 A343890 A343891 * A343893 A343894 A343895

Keyword

nonn

Author

Bernard Schott, May 06 2021

Status

approved