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Primes occurring in exactly three prime triples (p,q,r) with p<q<r=p+6.
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%I #21 Feb 16 2025 08:32:54

%S 11,13,17,103,107,1487,1873,3463,5653,15733,16063,16067,19423,19427,

%T 21017,22277,43783,43787,55337,79693,88813,101113,144167,165707,

%U 166847,195737,201827,225347,247607,257863,266683,268817,276043,284743

%N Primes occurring in exactly three prime triples (p,q,r) with p<q<r=p+6.

%C A098418(a(n)) = 3; subsequence of A098420.

%C This sequence consists of all integers of the form (prime(m)*prime(m+4)+36)/prime(m+2), for m>0, where prime(m) = A000040(m). Also note that the integers resulting from that rule equal prime(m+2), therefore a(n) also consists of all integers of the form sqrt[prime(m)*prime(m+4)+36]. - _Richard R. Forberg_, Jan 11 2016

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeTriplet.html">Prime Triplet</a>

%e A000040(27)=103: A007529(11)=103, A098414(10)=103 and A098415(9)=103, therefore 103 is a term.

%Y Cf. A098419, A098421, A098422.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Sep 07 2004