A342509 Primes p such that (p*s-q*r)/2 is prime, where p,q,r,s are consecutive primes.

43, 197, 313, 967, 1097, 1213, 1451, 1621, 2053, 2207, 2897, 2963, 3631, 3673, 4093, 4153, 4157, 4517, 4663, 4813, 4969, 5021, 5347, 5387, 5683, 6133, 6379, 6719, 6967, 7297, 7349, 7517, 7549, 8761, 8923, 9479, 10193, 10243, 10247, 11923, 12197, 12739, 13331, 13457, 13691, 14737, 15349, 15461

Offset

1,1

Links

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

Example

a(3) = 313 is a term because 313, 317, 331, 337 are consecutive primes with (313*337-317*331)/2 = 277 prime.

Maple

R:= NULL: count:= 0:
q:= 3: r:= 5: s:= 7:
while count < 100 do
  p:= q; q:= r; r:= s; s:= nextprime(s);
  if isprime((p*s-q*r)/2) then
     count:= count+1; R:= R, p;
  fi
od:
R;

Crossrefs

Cf. A342505, A342506, A342508.

Sequence in context: A142115 A141941 A197887 * A145650 A142527 A142161

Adjacent sequences: A342506 A342507 A342508 * A342510 A342511 A342512

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Mar 14 2021

Status

approved