Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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