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A128815 Numbers n such that n-th and (n+2)th triangular numbers sum up to a prime.

%I A128815 #9 Sep 04 2017 19:19:37
%S A128815 1,2,4,5,7,11,13,14,16,19,20,23,26,32,37,40,49,53,56,58,61,65,68,70,
%T A128815 74,76,77,79,88,89,98,100,104,109,110,116,118,130,137,140,142,146,149,
%U A128815 152,154,160,161,163,166,167,172,175,187,188,191,193,202,205,208,214,217
%N A128815 Numbers n such that n-th and (n+2)th triangular numbers sum up to a prime.
%C A128815 Or, numbers n such that 3+3n+n^2 is prime.
%H A128815 Robert Israel, <a href="/A128815/b128815.txt">Table of n, a(n) for n = 1..10000</a>
%F A128815 Tr(n)+Tr(n+2) is prime; A000217(n)+A000217(n+2) is prime.
%e A128815 7 is a term because 7*8/2+9*10/2=73 is prime;
%e A128815 11 is a term because 11*12/2+13*14/2=157 is prime.
%p A128815 select(t -> isprime(3+3*t+t^2), [$1..10000]); # _Robert Israel_, May 19 2014
%t A128815 Select[Range[300],PrimeQ[3+3#+#^2]&]
%t A128815 Position[Partition[Accumulate[Range[250]],3,1],_?(PrimeQ[#[[1]]+ #[[3]]]&), 1,Heads->False]//Flatten (* _Harvey P. Dale_, Sep 04 2017 *)
%Y A128815 Cf. A000217.
%K A128815 nonn
%O A128815 1,2
%A A128815 _Zak Seidov_, Apr 10 2007