User:Jason Kimberley/A002822

Cross References

		6n+1
		prime	not	union
6n-1	prime	A002822	A121763	A024898
	not	A121765	A060461	A046953
	union	A024899	A046954	A000027

Complex found

{<false, true>, <true, false>, <false, false>} = A067611 = A121765 $\cup$ A121763 $\cup$ A060461.

Not found

S{<true, true>, <false, false>} = A002822 $\cup$ A060461 = [1, 2, 3, 5, 7, 10, 12, 17, 18, 20, ...].

S{<false, true>, <true, false>} = A121763 $\cup$ A121765 = [4, 6, 8, 9, 11, 13, 14, 15, 16, 19, 21, 22, ...].

S{<false, true>, <true, true>, <false, false>} = [1, 2, 3, 5, 6, 7, 10, 11, 12, 13, 16, 17, 18, 20, 21, 23, 24, 25, 26, 27, ...]

S{<true, false>, <true, true>, <false, false>} = [1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 14, 15, 17, 18, 19, 20, 22, 23, 24, 25, ...]

S{<false, true>, <true, false>, <true, true>}

Magma Code

D := Set(Booleans());
P := Set(CartesianPower(D,2));
S := Subsets(P);
D; P; S;
state := func<n|<IsPrime(6*n-1),IsPrime(6*n+1)>>; 
//[*[*mp,[n:n in[1..100]|state(n) in mp]*]:mp in S*];
[*[*mp,s[1..Min(#s,10)]where s is [n:n in[1..50]|state(n) in mp]*]:mp in S*];

Magma Output

{ false, true }
{ <false, true>, <true, false>, <true, true>, <false, false> }
{
    {},
    { <true, true>, <false, false> },
    { <true, false> },
    { <false, true>, <true, false>, <false, false> },
    { <false, true>, <true, false> },
    { <true, false>, <false, false> },
    { <false, true> },
    { <false, true>, <true, true>, <false, false> },
    { <false, true>, <false, false> },
    { <false, false> },
    { <true, false>, <true, true>, <false, false> },
    { <false, true>, <true, true> },
    { <false, true>, <true, false>, <true, true>, <false, false> },
    { <false, true>, <true, false>, <true, true> },
    { <true, false>, <true, true> },
    { <true, true> }
}

[* [*
    {},
    []
*], [*
    { <true, true>, <false, false> },
    [ 1, 2, 3, 5, 7, 10, 12, 17, 18, 20 ]
*], [*
    { <true, false> },
    [ 4, 8, 9, 14, 15, 19, 22, 28, 29, 39 ]
*], [*
    { <false, true>, <true, false>, <false, false> },
    [ 4, 6, 8, 9, 11, 13, 14, 15, 16, 19 ]
*], [*
    { <false, true>, <true, false> },
    [ 4, 6, 8, 9, 11, 13, 14, 15, 16, 19 ]
*], [*
    { <true, false>, <false, false> },
    [ 4, 8, 9, 14, 15, 19, 20, 22, 24, 28 ]
*], [*
    { <false, true> },
    [ 6, 11, 13, 16, 21, 26, 27, 35, 37, 46 ]
*], [*
    { <false, true>, <true, true>, <false, false> },
    [ 1, 2, 3, 5, 6, 7, 10, 11, 12, 13 ]
*], [*
    { <false, true>, <false, false> },
    [ 6, 11, 13, 16, 20, 21, 24, 26, 27, 31 ]
*], [*
    { <false, false> },
    [ 20, 24, 31, 34, 36, 41, 48, 50 ]
*], [*
    { <true, false>, <true, true>, <false, false> },
    [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 12 ]
*], [*
    { <false, true>, <true, true> },
    [ 1, 2, 3, 5, 6, 7, 10, 11, 12, 13 ]
*], [*
    { <false, true>, <true, false>, <true, true>, <false, false> },
    [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]
*], [*
    { <false, true>, <true, false>, <true, true> },
    [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]
*], [*
    { <true, false>, <true, true> },
    [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 12 ]
*], [*
    { <true, true> },
    [ 1, 2, 3, 5, 7, 10, 12, 17, 18, 23 ]
*] *]