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Primes p such that there exists k such that p = prime(k) + prime(k+2) + prime(k+4).
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%I #27 Sep 15 2018 18:40:46

%S 23,61,71,109,157,173,199,211,223,239,269,283,373,383,421,443,487,503,

%T 547,599,691,701,719,829,991,1031,1153,1289,1297,1319,1399,1433,1453,

%U 1531,1579,1619,1667,1721,1823,1873,1907,1979,2029,2153,2251,2269,2381

%N Primes p such that there exists k such that p = prime(k) + prime(k+2) + prime(k+4).

%C Equivalently, primes that are the sum of 3 alternate primes. - _Muniru A Asiru_, Mar 05 2018

%H Harvey P. Dale, <a href="/A068363/b068363.txt">Table of n, a(n) for n = 1..1000</a>

%e From _Muniru A Asiru_, Mar 26 2018: (Start)

%e 23 is a term because prime(2) + prime(4) + prime(6) = 3 + 7 + 13 = 23, a prime.

%e 61 is a term because prime(6) + prime(8) + prime(10) = 13 + 19 + 29 = 61, a prime.

%e ... (End)

%p select(isprime,[seq(sum(ithprime(2*i-1+k),i=1..3),k=0..150)]); # _Muniru A Asiru_, Mar 05 2018

%t Select[#[[1]]+#[[3]]+#[[5]]&/@Partition[Prime[Range[200]],5,1],PrimeQ] (* _Harvey P. Dale_, Mar 16 2017 *)

%o (GAP) P:=Filtered([1..10000],IsPrime);;

%o Filtered(List([0..150],k->Sum([1..3],i->P[2*i-1+k])),IsPrime); # _Muniru A Asiru_, Mar 05 2018

%Y Cf. A068364.

%K easy,nonn

%O 1,1

%A _Benoit Cloitre_, Feb 28 2002