A333946 Perimeters of integer-sided triangles with prime inradius.

24, 30, 32, 36, 40, 42, 44, 56, 60, 64, 76, 80, 84, 96, 104, 108, 120, 132, 140, 144, 156, 168, 192, 204, 216, 220, 228, 240, 252, 276, 288, 312, 324, 336, 348, 360, 372, 396, 408, 420, 444, 480, 492, 516, 528, 552, 564, 576, 588, 624, 636, 660, 672, 684, 708, 732

Offset

1,1

Links

Table of n, a(n) for n=1..56.

Eric Weisstein's World of Mathematics, Incircle

Wikipedia, Incircle and excircles of a triangle

Wikipedia, Integer Triangle

Mathematica

Flatten[Table[If[Sum[Sum[(PrimePi[Sqrt[(n/2) (n/2 - i) (n/2 - k) (n/2 - (n - i - k))]/(n/2)] - PrimePi[Sqrt[(n/2) (n/2 - i) (n/2 - k) (n/2 - (n - i - k))]/(n/2) - 1]) (1 - Ceiling[Sqrt[(n/2) (n/2 - i) (n/2 - k) (n/2 - (n - i - k))]/(n/2)] + Floor[Sqrt[(n/2) (n/2 - i) (n/2 - k) (n/2 - (n - i - k))]/(n/2)]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}] > 0, n, {}], {n, 100}]]

Crossrefs

Cf. A005044, A333945 (integer inradius).

Sequence in context: A093455 A080564 A048260 * A354809 A337933 A114635

Adjacent sequences: A333943 A333944 A333945 * A333947 A333948 A333949

Keyword

nonn

Author

Wesley Ivan Hurt, Apr 11 2020

Status

approved