A173421 Triangular numbers which are sums of 5 consecutive primes.

28, 351, 1891, 4851, 7381, 9453, 15931, 26565, 31125, 68635, 90951, 110685, 130305, 140185, 218791, 224785, 240471, 243253, 309291, 341551, 466095, 497503, 780625, 889111, 899811, 1122751, 1188111, 1214461, 1269621, 1334161, 1408681, 1595791

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 18 2010

Keywords

• nonn

Examples

			28 = 2 + 3 + 5 + 7 + 11.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000217, A111163, A167788, A173420.

Programs

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

Mathematica

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# ]]&]
Select[Total/@Partition[Prime[Range[50000]],5,1],OddQ[Sqrt[1+8#]]&] (* Harvey P. Dale, Feb 08 2020 *)