A187797 Numbers having at least two different ordered partitions p+q and (p+2)+(q-2) where p, q, p+2 and q-2 are all prime.

10, 16, 18, 22, 24, 30, 34, 36, 42, 46, 48, 54, 60, 64, 66, 72, 76, 78, 84, 90, 102, 106, 108, 112, 114, 120, 126, 132, 138, 142, 144, 150, 154, 156, 162, 168, 174, 180, 184, 186, 192, 196, 198, 202, 204, 210, 216, 222, 228, 232, 234, 240, 244, 246, 252, 258, 264, 270, 274, 276, 282, 286

Offset: 1

Author

Bob Gilson, Aug 30 2013

Keywords

• nonn

Comments

Numbers k with at least one pair of externally tangent circles with radius sqrt(2) and center (p,q) where p and q are prime, p + q = k and p <= q. - Wesley Ivan Hurt, Aug 11 2020

Examples

			For n=10, the partition solutions are 3+7 and 5+5, giving p=3, q=7, p+2=5, q-2=5.
		

Programs

Maple

isA187797 := proc(n)
    local i,p,q ;
    for i from 1 do
        p := ithprime(i) ;
        q := n-p ;
        if q <= p+2 then
            return false;
        end if;
        if isprime(q) then
            if isprime(p+2) and isprime(q-2) then
                return true;
            end if;
        end if;
    end do:
    return false;
end proc:
for n from 4 to 600 do
    if isA187797(n) then
        printf("%d,",n);
    end if;
end do: # R. J. Mathar, Oct 03 2013

Mathematica

Table[If[Sum[(PrimePi[i] - PrimePi[i - 1]) (PrimePi[2 n - i] - PrimePi[2 n - i - 1]) (PrimePi[i + 2] - PrimePi[i + 1]) (PrimePi[2 n - i - 2] - PrimePi[2 n - i - 3]), {i, n - 2}] > 0, 2 n, {}], {n, 100}] // Flatten (* Wesley Ivan Hurt, Apr 13 2020 *)