

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.


1



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
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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 (r1)/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



