A341802 Primes p such that (q*s-p*r)/2 and |p*s-q*r|/2 are both prime, where p,q,r,s are consecutive primes.

313, 773, 1451, 1733, 2417, 2531, 3041, 3673, 7187, 7297, 7309, 7349, 9479, 9649, 10247, 10631, 11003, 11941, 12197, 12739, 13163, 14449, 16427, 16811, 19801, 21089, 22639, 24029, 24781, 26141, 26237, 26713, 29399, 30097, 30161, 30869, 31051, 33083, 33931, 34667, 37907, 40519, 40543, 40973, 41387

Offset

1,1

Comments

Intersection of A342505 with union of A342508 and A342509.

Links

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

Example

a(3) = 1451 is a term because 1451, 1453, 1459, 1471 are consecutive primes with (1453*1471-1451*1459)/2 = 10177 and |1451*1471-1453*1459|/2 = 7247 both 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(abs(p*s-q*r)/2) and isprime((q*s-p*r)/2) then
     count:= count+1; R:= R, p;
  fi
od:
R:

Mathematica

Select[Partition[Prime[Range[4500]], 4, 1], AllTrue[{(#[[2]]#[[4]]-#[[1]]#[[3]])/2, (#[[1]]#[[4]]- #[[2]] #[[3]])/2}, PrimeQ]&][[;; , 1]] (* Harvey P. Dale, Dec 24 2023 *)

Crossrefs

Cf. A342505, A342508, A342509.

Sequence in context: A087364 A090514 A068681 * A082436 A108845 A348170

Adjacent sequences: A341799 A341800 A341801 * A341803 A341804 A341805

Keyword

nonn

Author

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

Status

approved