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%I #15 Sep 08 2022 08:45:50
%S 28,351,1891,4851,7381,9453,15931,26565,31125,68635,90951,110685,
%T 130305,140185,218791,224785,240471,243253,309291,341551,466095,
%U 497503,780625,889111,899811,1122751,1188111,1214461,1269621,1334161,1408681,1595791
%N Triangular numbers which are sums of 5 consecutive primes.
%H Chai Wah Wu, <a href="/A173421/b173421.txt">Table of n, a(n) for n = 1..10000</a>
%e 28 = 2 + 3 + 5 + 7 + 11.
%t f[n_]:=Prime[n]+Prime[n+1]+Prime[n+2]+Prime[n+3]+Prime[n+4]; Select[Table[f[n],{n,9!}],IntegerQ[Sqrt[1+8# ]]&]
%t Select[Total/@Partition[Prime[Range[50000]],5,1],OddQ[Sqrt[1+8#]]&] (* _Harvey P. Dale_, Feb 08 2020 *)
%o (Magma) [ t: n in [1..28000] | IsSquare(8*t+1) where t is &+[NthPrime(n+s): s in [0..4]] ]; // _Bruno Berselli_, Apr 28 2011
%Y Cf. A000040, A000217, A111163, A167788, A173420.
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Feb 18 2010