A078723 a(n) = prime(n*(n+1)/2 + n).

3, 11, 23, 43, 71, 103, 149, 193, 251, 313, 389, 463, 569, 653, 761, 881, 1013, 1129, 1289, 1451, 1601, 1777, 1979, 2143, 2357, 2591, 2789, 3023, 3301, 3539, 3793, 4057, 4349, 4651, 4969, 5297, 5639, 5927, 6299, 6673, 7013, 7459, 7823, 8237, 8677, 9067, 9479

Offset: 1

Author

Cino Hilliard, Dec 20 2002

Keywords

• easy
• nonn

Comments

The sum of the reciprocals appears to converge.

Crossrefs

Primes in second diagonal from right in triangle in A078721.

Cf. A000040, A000096, A000217.

Programs

Mathematica

Table[Prime[(n(n+1))/2+n],{n,50}]  (* Harvey P. Dale, Jan 04 2011 *)

PARI

triprimes(n) = { sr = 0; for(j=1,n, x = j*(j+1)/2 +j; z = prime(x); sr+=1.0/z; print1(z" "); ); print(); print(sr); }

Formula

a(n) = A000040(A000096(n)).

Extensions

Offset changed to 1 by Alois P. Heinz, May 18 2019