A180686 Number of intersections of diagonals in the interior of a regular n-gon is prime for n.

5, 6, 14, 24, 44, 58, 72, 76, 80, 84, 86, 104, 128, 134, 138, 180, 186, 188, 218, 228, 246, 256, 266, 280, 300, 320, 352, 360, 380, 390, 408, 450, 480, 508, 518, 524, 526, 532, 546, 548, 552, 576, 584, 590, 604, 616, 630, 656, 658, 686, 712, 724, 726, 728, 730

Offset

1,1

References

Chris K. Caldwill & G. L. Honaker, Jr., Prime Curios!, The Dictionary of Prime Number Trivia, CreateSpace, Sept. 2009, p. 145.

Links

Table of n, a(n) for n=1..55.

Mathematica

del[m_, n_] := If[ Mod[n, m] == 0, 1, 0]; Int[n_] := If[n < 4, 0, Binomial[n, 4] + del[2, n] (-5n^3 + 45n^2 - 70n + 24)/24 - del[4, n] (3n/2) + del[6, n] (-45n^2 + 262n)/6 + del[12, n]*42n + del[18, n]*60n + del[24, n]*35n - del[30, n]*38n - del[42, n]*82n - del[60, n]*330n - del[84, n]*144n - del[90, n]*96n - del[120, n]*144n - del[210, n]*96n]; Select[ Range@ 759, PrimeQ@ Int@# &]

Crossrefs

Cf. A006561.

Sequence in context: A099330 A322479 A309480 * A308822 A289190 A145491

Adjacent sequences: A180683 A180684 A180685 * A180687 A180688 A180689

Keyword

nonn

Author

Robert G. Wilson v, Sep 16 2010

Status

approved