A351377 Primes p such that if the next prime is q, (q-p-1)! mod p is prime.

23, 61, 73, 83, 211, 409, 449, 509, 719, 787, 829, 887, 1039, 1237, 1409, 1459, 1627, 1831, 1879, 1913, 2089, 2179, 2297, 2521, 2647, 2663, 2699, 2879, 2909, 2927, 3011, 3041, 3049, 3121, 3209, 3331, 3361, 3433, 3491, 3583, 3659, 3719, 3863, 3889, 3967, 4289, 4327, 4349, 4363, 4373, 4583, 4679

Offset

1,1

Comments

Primes p such that the product of composites between p and the next prime has prime remainder on division by p.

Links

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

Example

a(3) = 73 is a term because 73 is prime, the next prime is 79, (79-73-1)! = 120 and 120 mod 73 = 47 is prime.

Maple

R:= NULL: count:= 0: q:= 2:
while count < 100 do
  p:= q; q:= nextprime(p);
  if isprime((q-p-1)! mod p) then
    count:= count+1; R:= R, p;
  fi
od:
R;

Crossrefs

Sequence in context: A055821 A080822 A068363 * A165286 A031342 A215166

Adjacent sequences: A351374 A351375 A351376 * A351378 A351379 A351380

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Mar 28 2022

Status

approved