A335623 Perimeters of integer-sided triangles such that the average of each pair of side lengths is prime.

6, 7, 9, 11, 15, 17, 19, 21, 25, 27, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133, 135, 137, 139, 141

Offset

1,1

Comments

Since the average of any two prime side lengths of an isosceles triangle is itself a prime, p, the perimeters 3p are in the sequence for all primes p.

Links

Table of n, a(n) for n=1..64.

Wikipedia, Integer Triangle

Mathematica

Table[If[Sum[Sum[(1 - Ceiling[(i + k)/2] + Floor[(i + k)/2]) (1 - Ceiling[(n - i)/2] + Floor[(n - i)/2]) (1 - Ceiling[(n - k)/2] + Floor[(n - k)/2]) (PrimePi[(i + k)/2] - PrimePi[(i + k)/2 - 1])*(PrimePi[(n - i)/2] - PrimePi[(n - i)/2 - 1])*(PrimePi[(n - k)/2] - PrimePi[(n - k)/2 - 1]) * Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}] > 0, n, {}], {n, 150}] // Flatten

Crossrefs

Cf. A005044 (Alcuin's sequence), A335622.

Sequence in context: A081053 A022892 A120164 * A074898 A258153 A175221

Adjacent sequences: A335620 A335621 A335622 * A335624 A335625 A335626

Keyword

nonn

Author

Wesley Ivan Hurt, Oct 02 2020

Status

approved