A340308 Primes p such that (p*q+r*s)/2 is prime, where q,r,s are the next 3 primes after p.

5, 7, 11, 23, 53, 73, 107, 137, 157, 179, 263, 281, 317, 373, 457, 593, 673, 821, 857, 1087, 1297, 1481, 1619, 1753, 1789, 2203, 2221, 2383, 2459, 2557, 2683, 2767, 2797, 2803, 2833, 3331, 3359, 3371, 3733, 3967, 4051, 4217, 4783, 4967, 5023, 5113, 5171, 5309, 5351, 5443, 5449, 5573, 6079, 6163

Offset

1,1

Links

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

Example

a(3) = 11 is a term because (11*13+17*19)/2 = 233 is prime.

Maple

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

Mathematica

Select[Partition[Prime[Range[1000]], 4, 1], PrimeQ[(#[[1]]#[[2]]+#[[3]]#[[4]])/2]&][[All, 1]] (* Harvey P. Dale, Feb 06 2023 *)

Prog

(PARI) isok(p) = if (isprime(p) && (p>2), my(q=nextprime(p+1), r=nextprime(q+1), s=nextprime(r+1)); isprime((p*q+r*s)/2)); \\ Michel Marcus, Jan 04 2021

Crossrefs

Cf. A340307.

Sequence in context: A005385 A181602 A075705 * A339096 A249735 A218394

Adjacent sequences: A340305 A340306 A340307 * A340309 A340310 A340311

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jan 03 2021

Status

approved