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A181902
Numbers k such that the k-th triangular number is prime or the arithmetic mean of 2 successive primes.
2
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
Sequence in context: A371685 A175095 A073216 * A295631 A278707 A294631
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms corrected by Gerasimov Sergey, R. J. Mathar, and Charles R Greathouse IV, Apr 04 2012
STATUS
approved