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%I #14 Sep 08 2022 08:45:50
%S 36,120,780,1596,1830,10440,12090,20706,22578,23436,34716,75466,
%T 101926,107880,115440,154290,191890,207690,231540,261726,271216,
%U 310866,313236,319600,384126,408156,512578,558096,653796,768180,824970,936396,1094460
%N Triangular numbers which are sums of 4 consecutive primes.
%H Chai Wah Wu, <a href="/A173420/b173420.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Table[Prime[n]+Prime[n+1]+Prime[n+2]+Prime[n+3],{n,2*8!}],IntegerQ[Sqrt[1+8# ]]&]
%t Select[Total/@Partition[Prime[Range[50000]],4,1],OddQ[Sqrt[1+8#]]&] (* _Harvey P. Dale_, May 29 2021 *)
%o (Magma) [ t: n in [1..25000] | IsSquare(8*t+1) where t is &+[NthPrime(n+s): s in [0..3]] ]; // _Bruno Berselli_, Apr 28 2011
%Y Cf. A000040, A000217, A111163, A167788.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Feb 18 2010
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