A331257 -id:A331257 - cp's OEIS frontend

A331258 Denominator of squared radius of inscribed circle of the n-th triangle with integer sides in the list given by A316841. Numerators are A331257.

12, 20, 3, 28, 28, 2, 4, 12, 5, 36, 5, 44, 3, 44, 44, 1, 52, 44, 3, 52, 7, 12, 52, 7, 52, 7, 4, 4, 52, 7, 20, 1, 68, 1, 60, 4, 2, 68, 20, 4, 68, 3, 76, 60, 4, 68, 9, 76, 5, 12, 68, 9, 68, 3, 76, 5, 68, 3, 76, 1, 4, 11, 68, 9, 76, 5, 84, 11, 92, 3, 76, 76, 1

Offset: 1

Hugo Pfoertner, Jan 26 2020

			See A331257.

Cf. A316841, A316843, A316844, A316845, A331257.

rh2(a,b,c)={my(s=(a+b+c)/2); (s-a)*(s-b)*(s-c)/s};
for(i=1,8, for(j=1,i, for(k=1,j, if(j+k>i, print1(denominator(rh2(i,j,k)),", ")))))

A140246 Decimal expansion of sqrt(15)/6.

Original entry on oeis.org

6, 4, 5, 4, 9, 7, 2, 2, 4, 3, 6, 7, 9, 0, 2, 8, 1, 4, 1, 9, 6, 5, 4, 4, 2, 3, 3, 2, 9, 7, 0, 6, 6, 6, 0, 1, 8, 0, 5, 4, 8, 6, 9, 5, 0, 8, 8, 1, 9, 3, 1, 8, 0, 4, 4, 3, 1, 2, 6, 2, 2, 9, 4, 3, 5, 2, 2, 4, 7, 1, 8, 1, 9, 8, 9, 4, 9, 6, 5, 0, 5, 5, 8, 6, 5, 4, 7, 8, 9, 6, 1, 4, 3, 1, 1, 2, 2, 5, 2, 9, 8, 6, 0, 5, 0

Offset: 0

Rick L. Shepherd, May 14 2008

Inradius of the obtuse scalene triangle with sides of lengths 2, 3 and 4, the scalene triangle with least integer side lengths. Per the Weisstein link, the inradius is the area divided by the semiperimeter.

			0.64549722436790281419654423329706660180548695088193180443126229435224718198...

Daniel Starodubtsev, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Inradius.
Index entries for algebraic numbers, degree 2

Cf. A140239, A140240, A140241, A140242, A140243, A140244, A140245, A140247, A140248, A140249, A088543, A010472.

Equals sqrt(A331257(8)/A331258(8)) (squared inradii of triangles with integer sides).

RealDigits[Sqrt[15]/6,10,120][[1]] (* Harvey P. Dale, Mar 31 2013 *)

PARI
```
sqrt(15)/6
```

sqrt(15)/6 = A010472/6 = 2*A140239/9.

cp's OEIS Frontend

A331258 Denominator of squared radius of inscribed circle of the n-th triangle with integer sides in the list given by A316841. Numerators are A331257.

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A140246 Decimal expansion of sqrt(15)/6.

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