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.

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

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

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

Adjacent sequences: A336297 A336298 A336299 * A336301 A336302 A336303

Keyword

nonn

Author

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

Status

approved