A152468 - OEIS

%I #21 Aug 21 2013 02:47:20

%S 5,7,11,13,19,29,31,43,53,59,67,73,79,107,109,113,127,137,149,151,157,

%T 163,179,191,211,223,229,263,269,307,311,349,353,359,379,383,401,409,

%U 419,433,443,449,461,467,479,521,523,541,557,569,571,577,599,613,619

%N Smallest of five consecutive primes whose sum is a prime.

%C Surprisingly many terms are also in A073681. - _Zak Seidov_, Dec 17 2012

%H Zak Seidov, <a href="/A152468/b152468.txt">Table of n, a(n) for n = 1..1000</a>

%t lst={};Do[p0=Prime[n];p1=Prime[n+1];p2=Prime[n+2];p3=Prime[n+3];p4=Prime[n+4];If[PrimeQ[p=p0+p1+p2+p3+p4],AppendTo[lst,p0]],{n,6!}];lst

%t Transpose[Select[Partition[Prime[Range[500]], 5, 1], PrimeQ[Total[#]] &]][[1]] (* _Harvey P. Dale_, Jun 05 2013 *)

%t Prime[Select[Range[150], PrimeQ[Sum[Prime[# + i], {i, 0, 4}]] &]] (* _Bruno Berselli_, Aug 21 2013 *)

%o (PARI) {a=2; b=3; c=5; d=7; e=11; for(n=1,100, s=a+b+c+d+e;

%o if(isprime(s), print1(a", ")); a=b; b=c; c=d; d=e; e=nextprime(e+2))} /* _Zak Seidov_, Dec 17 2012 */

%Y Cf. A073681, A034965, A180948, A189571, A180950, A226380.

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Dec 05 2008

%E More cross references from _Harvey P. Dale_, Jun 05 2013