A072184 Numbers n for which the prime circle problem has a slightly more complex solution than given in A072676. Complement of A072676.

17, 23, 32, 38, 44, 47, 59, 62, 65, 71, 77, 80, 86, 92, 101, 104, 107, 110, 122, 128, 137, 143, 146, 149, 152, 161, 164, 167, 170, 176, 179, 182, 185, 188, 191, 194, 197, 200, 203, 206, 212, 218, 224, 227, 233, 236, 239, 242, 245, 248, 251, 254, 257, 263, 266, 269, 272, 275, 278, 287, 290

Offset

0,1

Comments

n is in this sequence if (a) 2n+2i-1 and 2n+2i+1 are prime for some 0 < i < n and (b) there is an integer j < i such that the following four numbers are prime: 2n-1+2j, 2j+1, 2i+2j-1 and 2i+2j+1. The Mathematica program computes a prime circle for such n.

Links

Table of n, a(n) for n=0..60.

Eric Weisstein's World of Mathematics, Prime Circle.

Mathematica

n=17; lst={}; i=0; found=False; While[ !found&&i<n, i++; If[PrimeQ[2n+2i-1]&&PrimeQ[2n+2i+1], j=0; While[ !found&&j<i, j++; found=PrimeQ[2n-1+2j]&&PrimeQ[2j+1]&&PrimeQ[2i+2j-1]&&PrimeQ[2i+2j+1]]]]; If[found, lst=Flatten[Join[Table[{2k-1, 2i-2(k-j)}, {k, j, i-1}], Table[{2k-1, 2n-2(k-i)}, {k, i, n-1}], {2n-1, 2j}]], Print["no solution using this method"]]; If[found, i=j; While[n=i-1; n>0, i=0; found=False; While[i<n&&!found, i++; found=PrimeQ[2n+2i-1]&&PrimeQ[2n+2i+1]]; If[found, lst=Flatten[Append[Table[{2j-1, 2n-2(j-i)}, {j, i, n}], lst]]]]]; lst

Crossrefs

Cf. A051252.

Sequence in context: A145484 A080830 A165566 * A107644 A158710 A103805

Adjacent sequences: A072181 A072182 A072183 * A072185 A072186 A072187

Keyword

nonn

Author

T. D. Noe, Jul 01 2002

Status

approved