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A226196 Triangular numbers which are an average of four consecutive primes.

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