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A124000
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Semiprimes in A006987(n), or semiprime binomial coefficients: C(n,k), 2 <= k <= n-2.
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0
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6, 10, 15, 21, 35, 55, 91, 253, 703, 1081, 1711, 1891, 2701, 3403, 5671, 12403, 13861, 15931, 18721, 25651, 34453, 38503, 49141, 60031, 64261, 73153, 79003, 88831, 104653, 108811, 114481, 126253, 146611, 158203, 171991, 188191, 218791, 226801
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Conjecture: all a(n) except a(1) = 6 and a(2) = 10 are odd. Conjecture: all a(n) except a(5) = 35 are triangular numbers of the form p*(2p +/- 1) that belong to A068443(n) = {6, 10, 15, 21, 55, 91, 253, 703, 1081, 1711, 1891, 2701, ...} Triangular numbers with two distinct prime factors.
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MATHEMATICA
| semiPrimeQ[x_] := Plus @@ Last /@ FactorInteger[x] == 2; s = {}; Do[b = Binomial[n, k]; If[semiPrimeQ@b, AppendTo[s, b]], {n, 3, 1000}, {k, 2, n /2}]; s (* Robert G. Wilson v *)
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CROSSREFS
| Cf. A006987, A095147, A068443, A000217, A005382, A005384.
Sequence in context: A168102 A115744 A122783 * A068443 A113940 A099981
Adjacent sequences: A123997 A123998 A123999 * A124001 A124002 A124003
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KEYWORD
| nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 31 2006
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) Nov 03 2006
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