A156642 Number of decompositions of 4n+2 into unordered sums of two primes of the form 4k+3.

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

Offset: 0

Author

Vladimir Shevelev, Feb 12 2009

Keywords

• nonn

Comments

Conjecture. For n >= 1, a(n) > 0. This conjecture does not follow from the validity of the Goldbach binary conjecture because numbers of the form 4n+2, generally speaking, also have decompositions into sums of two primes of the form 4k+1.

Examples

			From _Lei Zhou_, Mar 19 2013: (Start)
n=1: 4n+2=6, 6=3+3; this is the only case that matches the definition, so a(1)=1;
n=3: 4n+2=14, 14=3+11=7+7; two instances found, so a(3)=2. (End)
		

Links

• Lei Zhou, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A002145, A002375, A061358, A002372, A045917, A214834, A217696.

Programs

Mathematica

Table[m = 4*n + 2; p1 = m + 1; ct = 0; While[p1 = p1 - 4; p2 = m - p1; p1 >= p2, If[PrimeQ[p1] && PrimeQ[p2], ct++]]; ct, {n, 1, 100}] (* Lei Zhou, Mar 19 2013 *)