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

1,1

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000217, A001043.

Sequence in context: A371685 A175095 A073216 * A295631 A278707 A294631

Adjacent sequences: A181899 A181900 A181901 * A181903 A181904 A181905

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 31 2012

Extensions

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

Status

approved