login
A034962
Primes that are the sum of three consecutive primes.
42
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
1,1
COMMENTS
Or, primes in A034961 (Sums of three consecutive primes). - Zak Seidov, Feb 16 2011
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
KEYWORD
nonn
AUTHOR
Patrick De Geest, Oct 15 1998
STATUS
approved