A124000 Semiprimes in A006987(n), or semiprime binomial coefficients: C(n,k), 2 <= k <= n-2.

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

Offset: 1

Author

Alexander Adamchuk, Oct 31 2006

Keywords

• nonn

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.

Besides 35 & 371953, all members were found by C(n, 2). - Robert G. Wilson v, Sep 16 2016

Of C(n,k), n: 4, 5, 6, 7, 11, 14, 23, 38, 47, 59, 62, 74, 83, 107, 158, 167, 179, 194, ..., . - Robert G. Wilson v, Sep 16 2016

Examples

			C(5,2) = 5!/(3!*2!) = 120/(6*2) = 10 is a semiprime (A001358), so 10 is in the sequence. - _Michael B. Porter_, Sep 17 2016
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..11521

Crossrefs

Cf. A006987, A095147, A068443, A000217, A005382, A005384, A001358.

Programs

Mathematica

s = {}; Do[b = Binomial[n, k]; If[PrimeOmega@ b == 2, AppendTo[s, b]; Print@ b], {n, 3, 10000}, {k, 2, n/2}]; s (* Robert G. Wilson v, Nov 03 2006; updated Sep 16 2016 *)

Formula

Intersection of A001358 and A006987. - Michael B. Porter, Sep 17 2016

Extensions

More terms from Robert G. Wilson v, Nov 03 2006