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A338324 Primes p such that there exist k and m with p < k < q < m < r such that p + k, q + k, q + m and r + m are all primes, where q and r are the next two primes after p.

%I A338324 #10 Oct 25 2020 00:01:24
%S A338324 23,29,47,199,523,709,797,809,991,1063,1163,1753,1789,1801,2161,2393,
%T A338324 2477,2549,2693,2917,3469,3491,4363,4423,4691,5039,5051,5081,5743,
%U A338324 6269,6607,7069,7351,7607,7883,8513,9103,9137,9391,9601,9859,10193,10343,10357,11003,11119,11321,11789,11941,13049
%N A338324 Primes p such that there exist k and m with p < k < q < m < r such that p + k, q + k, q + m and r + m are all primes, where q and r are the next two primes after p.
%C A338324 Members p of A336300 such that the next prime after p is also in A336300.
%H A338324 Robert Israel, <a href="/A338324/b338324.txt">Table of n, a(n) for n = 1..10000</a>
%e A338324 a(3) = 47 is in the sequence because 47 is prime, the next two primes are 53 and 59, and with k - 50 and m = 54, all of 47+50=97, 53+50=103, 53+54=107 and 59+54=113 are prime.
%p A338324 R:= NULL: count:= 0: thisp:= false:
%p A338324 q:= 2: r:= 3:
%p A338324 while count < 100 do
%p A338324   lastp:= thisp; thisp:= false;
%p A338324   p:= q; q:= r; r:= nextprime(r);
%p A338324   for k from (q+1)/2 to (r-1)/2 do
%p A338324     if isprime(q+2*k) and isprime(r+2*k) then
%p A338324        thisp:= true; break
%p A338324     fi
%p A338324   od;
%p A338324   if thisp and lastp then R:= R, p; count:= count+1 fi;
%p A338324 od:
%p A338324 R;
%Y A338324 Cf. A336300.
%K A338324 nonn
%O A338324 1,1
%A A338324 _J. M. Bergot_ and _Robert Israel_, Oct 22 2020