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A346416 Primes p such that the greatest perimeter of a triangle with prime sides including p and the next prime is prime.

%I A346416 #12 Dec 11 2024 12:53:07
%S A346416 5,11,13,17,19,37,41,43,47,59,71,89,103,109,113,137,139,149,163,167,
%T A346416 173,179,181,241,269,313,337,379,389,401,491,499,521,547,557,569,587,
%U A346416 599,607,613,617,631,643,673,677,701,739,773,787,811,839,877,883,887,929,941,953,971,977,983,1019,1021
%N A346416 Primes p such that the greatest perimeter of a triangle with prime sides including p and the next prime is prime.
%C A346416 If p is prime and q is the next prime, the greatest perimeter is p+q+r where r is the greatest prime < p+q.
%H A346416 Robert Israel, <a href="/A346416/b346416.txt">Table of n, a(n) for n = 1..10000</a>
%e A346416 a(3) = 13 is a term because the next prime is 17, the greatest prime < 13+17 is 29, and 13+17+29 = 59 is prime.
%p A346416 f:= proc(n) local p,q,r,s;
%p A346416   p:= ithprime(n);
%p A346416   q:= ithprime(n+1);
%p A346416   r:= prevprime(p+q);
%p A346416   s:= p+q+r;
%p A346416   if isprime(p+q+r) then return p fi
%p A346416 end proc:
%p A346416 map(f, [$1..500]);
%t A346416 Select[Partition[Prime[Range[200]],2,1],PrimeQ[Total[#]+NextPrime[Total[#],-1]]&][[;;,1]] (* _Harvey P. Dale_, Dec 11 2024 *)
%Y A346416 Cf. A096215.
%K A346416 nonn
%O A346416 1,1
%A A346416 _J. M. Bergot_ and _Robert Israel_, Jul 15 2021