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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. 0
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 32, 68, 152, 458 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

p1=p2 or p3=p4 allowed.

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

LINKS

Table of n, a(n) for n=1..14.

EXAMPLE

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.

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}]

CROSSREFS

Cf. A240713.

Sequence in context: A194402 A134930 A084562 * A276463 A187350 A118070

Adjacent sequences:  A240711 A240712 A240713 * A240715 A240716 A240717

KEYWORD

nonn,fini

AUTHOR

Lei Zhou, Apr 10 2014

STATUS

approved

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Last modified December 13 00:17 EST 2017. Contains 295954 sequences.