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
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jul 19 2022
STATUS
approved