A134143 Let T(n) = (p, p+2) denote the n-th pair of twin primes. Let S(n) = 2p+2 (see A054735). Then a(n) = number of ways of writing S(n) as S(i) + S(j) with i <= j < m.

0, 0, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 3, 2, 3, 1, 4, 3, 3, 3, 2, 6, 3, 5, 3, 3, 3, 3, 3, 8, 4, 2, 3, 3, 6, 4, 4, 6, 7, 8, 3, 6, 3, 9, 8, 7, 7, 5, 8, 4, 1, 6, 6, 3, 7, 1, 6, 6, 4, 8, 1, 5, 5, 8, 9, 11, 10, 6, 8, 16, 13, 9, 12, 6, 7, 8, 4, 16, 9, 6, 13, 10, 9, 5, 6, 6, 8, 11, 16, 11, 13, 6, 6, 6, 17, 9, 6, 6, 4

Offset: 1

Author

N. J. A. Sloane, Jan 25 2008

Keywords

• nonn

Comments

It is conjectured that a(n) > 0 for n >= 3.

Examples

			a(4) = 1 because S(4) = 17+19 = (5+7) + (11+13) = S(2)+S(3) and this is the only such way to write S(4) as the sum S(i) + S(j) for i <= j < 4.
		

References

• R. K. Guy, ed., Unsolved Problems, Western Number Theory Meeting, Las Vegas, 1988.

Links

• Dmitry Kamenetsky, Table of n, a(n) for n = 1..10000 (terms 1..680 from James A. Sellers and R. J. Mathar)

Crossrefs

Cf. A001359, A014574, A054735.

Programs

Maple

with(numtheory): Sset := {}; for i from 1 to 5000 do if ithprime(i + 1) - ithprime(i) = 2 then Sset := Sset union {2 ithprime(i) + 2} fi; od; Sset := convert(Sset, list): for n from 1 to nops(Sset) do count := 0: s := Sset[n]: for i from 1 to n do if member(s - Sset[i], Sset) and s - Sset[i] >= s/2 then count:=count + 1 fi: od: printf(`%d,`, count): od:# James Sellers, Jan 25 2008
A134143 := proc(n)
    local Sn, i, j, a;
    Sn := A054735(n);
    a := 0;
    for i from 1 to n-1 do
        for j from i to n-1 do
        if A054735(i)+A054735(j) = Sn then
            a := a+1;
        end if;
        end do:
    end do:
    a ;
end proc: # R. J. Mathar, Jan 25 2008

Extensions

Terms a(5) onwards computed by James Sellers and R. J. Mathar, Jan 25 2008