A342505 Primes p such that (q*s-p*r)/2 is prime, where p,q,r,s are consecutive primes.

3, 67, 313, 359, 443, 719, 773, 971, 991, 1063, 1163, 1229, 1361, 1433, 1451, 1459, 1697, 1733, 1877, 2087, 2273, 2377, 2417, 2473, 2531, 2659, 2879, 2953, 3041, 3203, 3559, 3673, 3719, 4003, 4091, 4691, 4861, 5107, 5179, 5261, 5783, 6217, 6317, 6373, 6833, 6907, 6971, 7187, 7297, 7309, 7349

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 and (317*337-313*331)/2 = 1613 is 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((q*s-p*r)/2) then
     count:= count+1; R:= R, p;
  fi
od:
R;

Crossrefs

Cf. A342504, A342508, A342509.

Sequence in context: A370659 A201857 A294395 * A186208 A217625 A238316

Adjacent sequences: A342502 A342503 A342504 * A342506 A342507 A342508

Keyword

nonn

Author

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

Status

approved