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A180686
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Positive integers k such that the number of intersections of diagonals in the interior of a regular k-gon is prime.
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1
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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
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history;
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OFFSET
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1,1
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REFERENCES
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Chris K. Caldwill & G. L. Honaker, Jr., Prime Curios!, The Dictionary of Prime Number Trivia, CreateSpace, Sept. 2009, p. 145.
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LINKS
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MATHEMATICA
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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@# &]
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PROG
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(Sage)
return Integer(binomial(k, 4) + (-5*k^3+45*k^2-70*k+24)*(k%2==0)/24
- 3*k*(k%4==0)/2 + (-45*k^2+262*k)*(k%6==0)/6 + 42*k*(k%12==0)
+ 60*k*(k%18==0) + 35*k*(k%24==0) - 38*k*(k%30==0)
- 82*k*(k%42==0) - 330*k*(k%60==0) - 144*k*(k%84==0)
- 96*k*(k%90==0) - 144*k*(k%120==0) - 96*k*(k%210==0)).is_prime()
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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