A240714 Even numbers whose unordered two primes decomposition set does not contain two groups of n = p1+p2 = p3+p4 such that |p1-p3| = 6 or 12.

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 32, 68, 152, 458

Offset: 1

Author

Lei Zhou, Apr 10 2014

Keywords

• nonn
• fini

Comments

p1=p2 or p3=p4 allowed.

Conjecture: this sequence is finite and all elements are listed.

Examples

			For number 152, 152 = 3+149 = 13+139 = 43+109 = 73+79.  The differences of adjacent smaller primes in each of the decomposition groups are 10, 30, 30 respectively.  None of them is 6 or 12.  So 152 is included.
		

Crossrefs

Cf. A240713.

Programs

Mathematica

n = 0; Table[
While[n++; s = 2*n; ct = 0; p = 1;
  While[p = NextPrime[p]; p <= n,
   If[PrimeQ[s - p], ok = 0; a1 = p - 12; b1 = s - a1; a2 = p - 6;
    b2 = s - a2; a3 = p + 6; b3 = s - a3; a4 = p + 12; b4 = s - a4;
    If[a1 > 0, If[PrimeQ[a1] && PrimeQ[b1], ok = 1]];
    If[a2 > 0, If[PrimeQ[a2] && PrimeQ[b2], ok = 1]];
    If[a3 <= n, If[PrimeQ[a3] && PrimeQ[b3], ok = 1]];
    If[a4 <= n, If[PrimeQ[a4] && PrimeQ[b4], ok = 1]];
    If[ok == 1, ct++]]]; ct != 0]; s, {k, 1, 14}]