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A336300
Primes p such that there exists k with p < k < q such that p+k and q+k are prime, where q is the next prime after p.
2
5, 23, 29, 31, 47, 53, 73, 83, 113, 131, 139, 151, 173, 199, 211, 251, 293, 317, 359, 373, 467, 491, 509, 523, 541, 557, 593, 607, 647, 659, 683, 709, 719, 761, 773, 797, 809, 811, 863, 911, 991, 997, 1063, 1069, 1103, 1117, 1163, 1171, 1187, 1201, 1231, 1259, 1307, 1327, 1409, 1439, 1459, 1499
OFFSET
1,1
COMMENTS
There may be more than one such k: thus for a(17) = 293, k = 294, 300, and 306 all work.
LINKS
EXAMPLE
a(4)=31 is included because 31 is prime, the next prime after 31 is 37, and with k=36 we have 31+36=67 and 37+36=73 both prime.
MAPLE
P:= [seq(ithprime(i), i=2..1000)]:
R:= NULL:
for i from 1 to nops(P)-1 do
for k from ceil(P[i]/2) to floor(P[i+1]/2) do
if isprime(P[i]+2*k) and isprime(P[i+1]+2*k) then
R:= R, P[i]; break
fi
od;
od:
R;
CROSSREFS
Includes A069142.
Sequence in context: A196243 A018527 A084411 * A243458 A067367 A140386
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Oct 22 2020
STATUS
approved