A181902 Numbers k such that the k-th triangular number is prime or the arithmetic mean of 2 successive primes.

2, 3, 5, 6, 9, 14, 15, 21, 24, 26, 30, 38, 39, 41, 48, 53, 54, 78, 80, 81, 87, 89, 92, 104, 116, 117, 119, 121, 122, 125, 126, 146, 149, 150, 153, 156, 158, 164, 165, 170, 171, 185, 186, 194, 206, 210, 218, 245, 248, 252, 255, 258, 270, 281, 285, 290, 296, 297

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 31 2012

Keywords

• nonn

Examples

			2 is a term because 2*(2+1)/2 = 3 is prime,
3 is a term because 3*(3+1)/2 = (5+7)/2,
5 is a term because 5*(5+1)/2 = (13+17)/2.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000217, A001043.

Programs

Magma

[2] cat [n: n in [3..320] | 2*t eq PreviousPrime(t)+NextPrime(t) where t is n*(n+1) div 2]; // Bruno Berselli, Apr 04 2012

Mathematica

a = {2}; For[n = 1, n < 320, n++, t = n*(n + 1)/2;
If[t == (NextPrime[t] + NextPrime[t, -1])/2, AppendTo[a, n],
  1]]; Print[a]; (* David Scambler, Apr 02 2012 *)

PARI

is(n)=n*=(n+1)/2;n>1&&2*n==nextprime(n)+precprime(n) \\ Charles R Greathouse IV, Apr 04 2012

Extensions

Terms corrected by Gerasimov Sergey, R. J. Mathar, and Charles R Greathouse IV, Apr 04 2012