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%I #23 Dec 06 2012 14:29:34
%S 10,19,47,43,91,127,115,187,215,271,235,335,403,385,475,455,727,655,
%T 695,805,595,895,835,875,1085,1235,1195,1309,1015,1295,1405,1675,1435,
%U 1375,2005,1615,1715,1975,2015,1925,2335,1855,2255,2035,2585,2575,2765,2555
%N Smallest integer expressible as 2p + 3q (p, q primes not necessarily distinct) in exactly n ways.
%H Zak Seidov, <a href="/A219959/b219959.txt">Table of n, a(n) for n = 1..2000</a>
%e a(1) = 10 because it can be expressed as 2p + 3q in only one way, 2 * 2 + 3 * 2, and is the smallest integer for which this is the case.
%e a(2) = 19 because it can be expressed as 2p + 3q in only two ways, 2 * 2 + 3 * 5 = 2 * 5 + 3 * 3, and is the smallest integer for which this is the case.
%t mx = 10000; s = Table[0, {mx}]; Do[a = 2 Prime[i] + 3 Prime[k]; s[[a]]++, {k, PrimePi[(mx - 4)/3]}, {i, PrimePi[(mx - 3 Prime[k])/2]}];Table[Position[s, n][[1, 1]], {n, 50}]
%Y Cf. A079026, A219955, A219956, A219957, A219958.
%K nonn
%O 1,1
%A _Zak Seidov_, Dec 02 2012
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