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.

23, 29, 47, 199, 523, 709, 797, 809, 991, 1063, 1163, 1753, 1789, 1801, 2161, 2393, 2477, 2549, 2693, 2917, 3469, 3491, 4363, 4423, 4691, 5039, 5051, 5081, 5743, 6269, 6607, 7069, 7351, 7607, 7883, 8513, 9103, 9137, 9391, 9601, 9859, 10193, 10343, 10357, 11003, 11119, 11321, 11789, 11941, 13049

Offset: 1

Author

J. M. Bergot and Robert Israel, Oct 22 2020

Keywords

• nonn

Comments

Members p of A336300 such that the next prime after p is also in A336300.

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A336300.

Programs

Maple

R:= NULL: count:= 0: thisp:= false:
q:= 2: r:= 3:
while count < 100 do
  lastp:= thisp; thisp:= false;
  p:= q; q:= r; r:= nextprime(r);
  for k from (q+1)/2 to (r-1)/2 do
    if isprime(q+2*k) and isprime(r+2*k) then
       thisp:= true; break
    fi
  od;
  if thisp and lastp then R:= R, p; count:= count+1 fi;
od:
R;