A165966 Triangular numbers that are sums of twin prime pairs.

36, 120, 276, 300, 2556, 3240, 5460, 8256, 12720, 23436, 26796, 34980, 41616, 46056, 56616, 59340, 103740, 122760, 139656, 147696, 157080, 185136, 195000, 231540, 277140, 333336, 353220, 386760, 401856, 516636, 609960, 860016, 1001820

Offset: 1

Author

Zak Seidov, Oct 01 2009

Keywords

• nonn

Comments

All terms are multiples of 12.

Examples

			36 = 8*9/2 is a term since it is triangular and the sum of the twin primes 17 and 19.
120 = 15*16/2 is a term since it is triangular and the sum of the twin primes 59 and 61.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A111163 and of A054735.

Cf. A000217, A001359, A105174.

Programs

Mathematica

tri[n_] := n*(n+1)/2; Select[tri /@ Range[10^3], And @@ PrimeQ[#/2 + {-1, 1}] &] (* Amiram Eldar, Dec 27 2019 *)

PARI

lista(nn) = {for (n = 1, nn, trg = n*(n+1)/2; if (!(trg % 2) && isprime(trg/2-1) && isprime(trg/2+1), print1(trg, ", ")););} \\ Michel Marcus, Oct 16 2013

Formula

a(n) = A105174(n)*(A105174(n) + 1)/2.