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

1,1

Comments

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

Links

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

Example

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.

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;

Crossrefs

Cf. A336300.

Sequence in context: A085713 A102904 A108249 * A232725 A045120 A174260

Adjacent sequences: A338321 A338322 A338323 * A338325 A338326 A338327

Keyword

nonn

Author

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

Status

approved