A034962 Primes that are the sum of three consecutive primes.

23, 31, 41, 59, 71, 83, 97, 109, 131, 173, 199, 211, 223, 251, 269, 311, 349, 439, 457, 487, 503, 607, 661, 701, 829, 857, 883, 911, 941, 1033, 1049, 1061, 1151, 1187, 1229, 1249, 1303, 1367, 1381, 1409, 1433, 1493, 1511, 1553, 1667, 1867, 1931, 1973, 1993

Offset: 1

Author

Patrick De Geest, Oct 15 1998

Keywords

• nonn

Comments

Or, primes in A034961 (Sums of three consecutive primes). - Zak Seidov, Feb 16 2011

Examples

			E.g., 131 = 41 + 43 + 47.
A034962(n) = p+q+r, where p = A073681(n), and p<q<r are three consecutive primes. - _Zak Seidov_, Mar 09 2009
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000
• Zak Seidov, Table of n, primepi(A073681(n)), primepi(A034962(n)), A073681(n), A152469(n), A152470(n), A034962(n) for n = 1..10000
• Zak Seidov, Table of a(1000*k) for k=1..1346.

Crossrefs

Cf. A001043, A011974, A034707, A034961. Different from A050207.

Cf. A073681 (smallest of three consecutive primes whose sum is a prime).

Programs

Magma

[a: n in [1..150] | IsPrime(a) where a is NthPrime(n)+NthPrime(n+1)+NthPrime(n+2)]; // Vincenzo Librandi, Jun 23 2016

Maple

a:=proc(n) if isprime(ithprime(n)+ithprime(n+1)+ithprime(n+2))=true then ithprime(n)+ithprime(n+1)+ithprime(n+2) else fi end: seq(a(n), n=1..120); # Emeric Deutsch, Apr 24 2006

Mathematica

a = {}; Do[k = Prime[x] + Prime[x + 1] + Prime[x + 2]; If[PrimeQ[k], AppendTo[a, k]], {x, 1, 350}]; a (* Artur Jasinski, Jan 27 2007 *)
Select[(Plus@@@Partition[Prime[Range[200]],3,1]),PrimeQ] (* Zak Seidov, Feb 07 2012 *)
Select[ListConvolve[{1,1,1},Prime[Range[200]]],PrimeQ] (* Harvey P. Dale, Jul 12 2013 *)

PARI

forprime(p=2,1000, p2=nextprime(p+1); p3=nextprime(p2+1); q=p+p2+p3; if(isprime(q),print1(q",")) ) \\ Max Alekseyev, Jan 26 2007

PARI

{p=2;q=3;for(n=1,100,r=nextprime(q+1); if(isprime(t=p+q+r),print1(t","));p=q;q=r;)} \\ Zak Seidov, Mar 09 2009

Python

from itertools import count, islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    p, q, r = 2, 3, 5
    while True:
        if isprime(p+q+r): yield p+q+r
        p, q, r = q, r, nextprime(r)
print(list(islice(agen(), 50))) # Michael S. Branicky, Dec 27 2022