A034962 - OEIS

%I #43 Dec 28 2022 01:57:19

%S 23,31,41,59,71,83,97,109,131,173,199,211,223,251,269,311,349,439,457,

%T 487,503,607,661,701,829,857,883,911,941,1033,1049,1061,1151,1187,

%U 1229,1249,1303,1367,1381,1409,1433,1493,1511,1553,1667,1867,1931,1973,1993

%N Primes that are the sum of three consecutive primes.

%C Or, primes in A034961 (Sums of three consecutive primes). - _Zak Seidov_, Feb 16 2011

%H Zak Seidov, <a href="/A034962/b034962.txt">Table of n, a(n) for n = 1..10000</a>

%H Zak Seidov, <a href="/A034962/a034962.txt">Table of n, primepi(A073681(n)), primepi(A034962(n)), A073681(n), A152469(n), A152470(n), A034962(n) for n = 1..10000</a>

%H Zak Seidov, <a href="/A034962/a034962_1.txt">Table of a(1000*k) for k=1..1346. </a>

%e E.g., 131 = 41 + 43 + 47.

%e A034962(n) = p+q+r, where p = A073681(n), and p<q<r are three consecutive primes. - _Zak Seidov_, Mar 09 2009

%p 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

%t 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 *)

%t Select[(Plus@@@Partition[Prime[Range[200]],3,1]),PrimeQ] (* _Zak Seidov_, Feb 07 2012 *)

%t Select[ListConvolve[{1,1,1},Prime[Range[200]]],PrimeQ] (* _Harvey P. Dale_, Jul 12 2013 *)

%o (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

%o (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

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

%o (Python)

%o from itertools import count, islice

%o from sympy import isprime, nextprime

%o def agen(): # generator of terms

%o     p, q, r = 2, 3, 5

%o     while True:

%o         if isprime(p+q+r): yield p+q+r

%o         p, q, r = q, r, nextprime(r)

%o print(list(islice(agen(), 50))) # _Michael S. Branicky_, Dec 27 2022

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

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

%K nonn

%O 1,1

%A _Patrick De Geest_, Oct 15 1998