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A152469 Second smallest of three consecutive primes whose sum is a prime.

%I A152469 #8 May 08 2021 16:18:36
%S A152469 7,11,13,19,23,29,31,37,43,59,67,71,73,83,89,103,113,149,151,163,167,
%T A152469 199,223,233,277,283,293,307,313,347,349,353,383,397,409,419,433,457,
%U A152469 461,467,479,499,503,521,557,619,643,659,661,673,709,727,751,757,761
%N A152469 Second smallest of three consecutive primes whose sum is a prime.
%H A152469 Harvey P. Dale, <a href="/A152469/b152469.txt">Table of n, a(n) for n = 1..1000</a>
%p A152469 t0:=[];
%p A152469 t1:=[];
%p A152469 t2:=[];
%p A152469 t3:=[];
%p A152469 for i from 1 to 1000 do
%p A152469 t3:=ithprime(i)+ithprime(i+1)+ithprime(i+2);
%p A152469 if isprime(t3) then
%p A152469 t0:=[op(t0),i];
%p A152469 t1:=[op(t1),ithprime(i)];
%p A152469 t2:=[op(t2),ithprime(i+1)];
%p A152469 t3:=[op(t2),ithprime(i+2)];
%p A152469 fi;
%p A152469 od:
%p A152469 t2;
%t A152469 lst={};Do[p0=Prime[n];p1=Prime[n+1];p2=Prime[n+2];If[PrimeQ[p0+p1+p2],AppendTo[lst,p1]],{n,6!}];lst
%t A152469 Select[Partition[Prime[Range[200]],3,1],PrimeQ[Total[#]]&][[All,2]] (* _Harvey P. Dale_, May 08 2021 *)
%Y A152469 Cf. A073681, A072225, A152468, A152470.
%K A152469 nonn
%O A152469 1,1
%A A152469 _Vladimir Joseph Stephan Orlovsky_, Dec 05 2008