A173423 Triangular numbers which are sums of 6 consecutive primes.

630, 990, 2926, 4950, 5886, 12720, 24090, 44850, 60726, 81810, 107416, 128778, 152076, 168490, 177906, 202566, 217470, 258840, 277140, 301476, 314028, 408156, 499500, 613278, 695610, 875826, 903840, 940506, 1205128, 1332528, 1405326

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 (n = 1..528 from Robert Israel)

Crossrefs

Cf. A000040, A000217, A111163, A167788, A173420, A173421.

Programs

Magma

[ t: n in [1..22000] | IsSquare(8*t+1) where t is &+[NthPrime(n+s): s in [0..5]] ]; // Bruno Berselli, Apr 28 2011

Maple

Primes:= select(isprime, [2,seq(i,i=3..10^7,2)]):
P6:= Primes[1..-6]+Primes[2..-5]+Primes[3..-4]+Primes[4..-3]+Primes[5..-2]+Primes[6..-1]:
select(t -> issqr(8*t+1),P6): # Robert Israel, Sep 26 2016

Mathematica

f[n_]:=Prime[n]+Prime[n+1]+Prime[n+2]+Prime[n+3]+Prime[n+4]+Prime[n+5]; Select[Table[f[n],{n,9!}],IntegerQ[Sqrt[1+8# ]]&]
Select[Total/@Partition[Prime[Range[25000]],6,1],OddQ[Sqrt[8#+1]]&] (* Harvey P. Dale, Mar 06 2023 *)