%I #13 Dec 18 2015 12:07:58
%S 15,55,105,120,253,595,1225,1485,2080,2211,3321,4371,5460,6786,7381,
%T 7503,10731,11935,12246,16290,18915,24531,24753,27966,36585,44850,
%U 51360,55278,55945,56953,60031,64980,68265,69006,70125,75078,86736,87153,92235,94830,98790,111628
%N Triangular numbers which are an average of four consecutive primes.
%H Zak Seidov, <a href="/A226196/b226196.txt">Table of n, a(n) for n = 1..3000</a>
%F a(n) = A000217(A226153(n)).
%p A000217inv:=proc(n)
%p local t1;
%p t1:=floor(sqrt(2*n));
%p if n = t1*(t1+1)/2 then
%p return t1 ;
%p else
%p return -1;
%p end if;
%p end proc:
%p for n from 1 to 90000 do
%p s := A034963(n)/4 ;
%p if type(s, 'integer') then
%p tr := A000217inv(s) ;
%p if tr >= 0 then
%p printf("%d, ", s) ;
%p end if;
%p end if;
%p end do: # _R. J. Mathar_, Jun 06 2013
%t Select[Mean/@Partition[Prime[Range[20000]],4,1],OddQ[Sqrt[8#+1]]&] (* _Harvey P. Dale_, Dec 18 2015 *)
%Y Cf. A000217, A034963, A226153.
%K nonn
%O 1,1
%A _Alex Ratushnyak_, May 30 2013