A173420 Triangular numbers which are sums of 4 consecutive primes.

36, 120, 780, 1596, 1830, 10440, 12090, 20706, 22578, 23436, 34716, 75466, 101926, 107880, 115440, 154290, 191890, 207690, 231540, 261726, 271216, 310866, 313236, 319600, 384126, 408156, 512578, 558096, 653796, 768180, 824970, 936396, 1094460

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 18 2010

Keywords

• nonn

Links

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

Crossrefs

Cf. A000040, A000217, A111163, A167788.

Programs

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

Mathematica

Select[Table[Prime[n]+Prime[n+1]+Prime[n+2]+Prime[n+3],{n,2*8!}],IntegerQ[Sqrt[1+8# ]]&]
Select[Total/@Partition[Prime[Range[50000]],4,1],OddQ[Sqrt[1+8#]]&] (* Harvey P. Dale, May 29 2021 *)