A342506 Primes p such that (p*s+q*r)/2 is prime, where p,q,r,s are consecutive primes.

5, 7, 13, 97, 107, 157, 223, 311, 353, 419, 479, 541, 673, 691, 701, 839, 877, 1049, 1193, 1297, 1423, 1559, 1747, 1787, 2017, 2239, 2341, 2383, 2459, 2633, 2719, 2797, 2833, 2851, 3121, 3209, 3359, 3391, 3581, 3613, 3617, 3671, 4219, 4261, 4729, 4831, 4933, 4993, 5023, 5309, 5393, 5657, 5867

Offset

1,1

Links

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

Example

a(3) = 13 is a term because 13, 17, 19, 23 are consecutive primes with (13*23+17*19)/2 = 311 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. A342504, A342508.

Sequence in context: A102872 A102873 A356847 * A158892 A106022 A279795

Adjacent sequences: A342503 A342504 A342505 * A342507 A342508 A342509

Keyword

nonn

Author

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

Status

approved