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

1,7

Comments

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

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)

Example

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.

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 A. 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

Crossrefs

Cf. A001359, A014574, A054735.

Sequence in context: A338169 A243847 A245421 * A295555 A085684 A141604

Adjacent sequences: A134140 A134141 A134142 * A134144 A134145 A134146

Keyword

nonn

Author

N. J. A. Sloane, Jan 25 2008

Extensions

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

Status

approved