A173420 -id:A173420 - cp's OEIS frontend

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

Vladimir Joseph Stephan Orlovsky, Feb 18 2010

nonn

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

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

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

[ t: n in [1..28000] | IsSquare(8*t+1) where t is &+[NthPrime(n+s): s in [0..4]] ]; // Bruno Berselli, Apr 28 2011

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 *)

A173423 Triangular numbers which are sums of 6 consecutive primes.

Original entry on oeis.org

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

Vladimir Joseph Stephan Orlovsky, Feb 18 2010

nonn

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

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

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

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

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 *)

cp's OEIS Frontend

A173421 Triangular numbers which are sums of 5 consecutive primes.

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