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

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..528 from Robert Israel)

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A256937 A177421 A333503 * A295769 A110904 A171258

Adjacent sequences: A173420 A173421 A173422 * A173424 A173425 A173426

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Feb 18 2010

Status

approved