BBC Russian

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

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.

EXAMPLE

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

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 *)

PROG

(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

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

(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

CROSSREFS

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

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

Sequence in context: A026051 A141818 A060328 * A133659 A309354 A240725

Adjacent sequences: A034959 A034960 A034961 * A034963 A034964 A034965

KEYWORD

nonn

AUTHOR

Patrick De Geest, Oct 15 1998

STATUS

approved