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%I #16 Feb 19 2022 14:29:49
%S 3,5,17,29,59,137,149,179,197,227,269,419,599,617,659,809,1019,1049,
%T 1277,1289,1607,1787,1997,2129,2237,2267,2657,2789,3167,3257,3299,
%U 3329,3359,3527,3557,3917,3929,4217,4229,4259,4547,4637,4649,4787,4799,5009,5099
%N Initial members of prime triples (p, p+2, p+14).
%C According to the k-tuple conjecture this sequence is theoretically infinite.
%H Chris K. Caldwell <a href="https://primes.utm.edu/glossary/xpage/PrimeKtupleConjecture.html">prime k-tuple conjecture</a>
%H Chris K. Caldwell <a href="https://primes.utm.edu/glossary/xpage/ktuple.html">k-tuple</a>
%p for a from 3 to 1000 by 2 do
%p if isprime(a) and isprime(a+2) and isprime(a+14) then
%p print(a);
%p end if
%p end do
%p # second Maple program:
%p q:= p-> andmap(isprime, [p, p+2, p+14]):
%p select(q, [$1..10000])[]; # _Alois P. Heinz_, Jan 28 2022
%t Select[Range[7000], And @@ PrimeQ[# + {0, 2, 14}] &] (* _Amiram Eldar_, Jan 20 2022 *)
%Y Cf. A022004 (p,p+2,p+6), A046134 (p,p+2,p+8), A046135 (p,p+2,p+12).
%K nonn
%O 1,1
%A _Matt C. Anderson_, Jan 19 2022
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