A358447 Numbers k such that there exist primes p, q, r, s with k = p + q = r + s = p*q - r*s.

16, 24, 96, 120, 240, 264, 504, 744, 840, 1080, 1104, 1416, 1440, 1680, 2256, 2280, 2520, 2760, 2856, 3120, 3264, 3456, 3576, 3696, 3864, 3960, 4296, 4440, 4536, 4584, 4800, 5040, 5496, 5640, 5880, 6720, 6960, 7224, 7800, 8280, 8904, 8976, 9240, 9480, 9984, 10080, 10296, 10656, 10824, 10920

Offset

1,1

Comments

All terms are divisible by 8.

Links

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

Example

a(3) = 96 is a term because 96 = 43 + 53 = 37 + 59 = 43*53 - 37*59 with 43, 53, 37 and 59 prime.

Maple

filter:= proc(n) local s, t;
   for s in numtheory:-divisors(n/4) do
     t:= n/(4*s);
     if andmap(isprime, [2*s*t+s-t, 2*s*t-s+t, 2*s*t-s-t, 2*s*t+s+t]) then
        return  true
     fi
    od;
false
end proc:
select(filter, [seq(i, i=8..20000, 8)]);

Crossrefs

Sequence in context: A024588 A334229 A335296 * A120468 A166629 A066261

Adjacent sequences: A358444 A358445 A358446 * A358448 A358449 A358450

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Nov 17 2022

Status

approved