A130178 Triangular numbers which are the average of two consecutive primes.

6, 15, 21, 45, 105, 120, 231, 300, 351, 465, 741, 780, 861, 1176, 1431, 1485, 3081, 3240, 3321, 3828, 4005, 4278, 5460, 6786, 6903, 7140, 7381, 7503, 7875, 8001, 10731, 11175, 11325, 11781, 12246, 12561, 13530, 13695, 14535, 14706, 17205, 17391

Offset

1,1

Comments

Intersection of A000217 (triangular numbers) and A024675 (average of two consecutive primes).

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Example

6-/+1, 15-/+2,..., 300-/+7 are pairs of consecutive primes.

Mathematica

Select[Mean/@Partition[Prime[Range[2500]], 2, 1], OddQ[Sqrt[8#+1]]&] (* or *) Select[Accumulate[Range[200]], #==(NextPrime[#]+NextPrime[#, -1])/2&] (* Harvey P. Dale, Oct 15 2025 *)

Crossrefs

Cf. A000217, A024675.

Sequence in context: A357325 A362211 A072521 * A100410 A095032 A227610

Adjacent sequences: A130175 A130176 A130177 * A130179 A130180 A130181

Keyword

nonn

Author

Zak Seidov, May 14 2007

Status

approved