A355696 First of four consecutive primes p,q,r,s such that the sum of numerator and denominator of p/q + q/r, p/q + r/s, and q/r + r/s, are all prime.

11, 29, 1811, 2531, 3373, 4153, 5927, 7121, 7127, 8419, 11743, 14347, 14419, 17659, 26357, 26729, 33529, 43051, 57809, 61223, 81689, 87991, 99527, 99529, 113123, 125107, 141959, 146359, 152993, 154849, 162629, 165709, 168323, 197927, 198437, 205483, 207679, 207821, 216851, 216991, 221729, 228457

Offset

1,1

Comments

First of four consecutive primes p,q,r,s such that p*r + q^2 + q*r, q*s + r^2 + r*s, and p*s + q*r + q*s are all primes.

Links

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

Example

a(2) = 11 is a term because 11, 13, 17, 19 are consecutive primes: 11/13 + 13/17 = 356/221 with 356 + 221 = 577 prime, 11/13 + 17/19 = 430/247 with 430 + 247 = 677 prime, and 13/17 + 17/19 = 536/323 with 536 + 323 = 859 prime.

Maple

R:= NULL: count:= 0:
q:= 2: r:= 3: s:= 5:
while count < 50 do
  p:= q; q:= r: r:= s: s:= nextprime(s);
  if isprime(p*r+q^2+q*r) and isprime(q*s+r^2+r*s) and isprime(p*s+q*r+q*s) then
       count:= count+1; R:= R, p;
    fi
od:
R;

Mathematica

f[v_] := Module[{p, q, r, s}, {p, q, r, s} = v; PrimeQ[p*r+q^2+q*r] && PrimeQ[q*s+r^2+r*s] && PrimeQ[p*s+q*r+q*s]]; Select[Partition[Prime[Range[20000]], 4, 1], f[#] &][[;; , 1]] (* Amiram Eldar, Jul 20 2022 *)

Crossrefs

Sequence in context: A027758 A351353 A285992 * A271348 A057739 A146751

Adjacent sequences: A355693 A355694 A355695 * A355697 A355698 A355699

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jul 19 2022

Status

approved