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%I #14 Feb 18 2016 14:02:28
%S 2,43,23,0,1109,1187,929,0,4973,1291,11197,0,26099,15583,4423,0,42139,
%T 10729,21283,0,36899,27179,21563,0,24359,33863,27361,0,223423,51239,
%U 293467,42043,67699,56503,118361,0,80449,94693,136739,0,127837,136991,387913,0,304259,192013,321721,0,339517,357683
%N Smallest prime that is the (sum, k*prime(k),k=m,..n+m-1) for some m, or 0 if no such m exists.
%C Smallest prime that is the sum of n consecutive terms of A033286.
%C Apparently a(n) exists for any odd n.
%C Values of m = {1, 3, 1, 0, 7, 6, 4, 0, 9, 2, 12, 0, 17, 11, 2, 0, 17, 4, 8, 0, 11, 7, 4, 0, 3, 5, 2, 0, 27, 5, 30, 1, 5, 2, 10, 0, 3, 4, 8, 0, 5, 5, 22, 0, 15, 6, 14, 0, 13, 13, ...}. - _Michael De Vlieger_, Feb 05 2016
%e n=1: m=1 and 1*prime(1) = 1*2 = 2 = a(1),
%e n=2: m=3 and 3*prime(3)+4*prime(4) = 3*5+4*7 = 43 = a(2),
%e n=3: m=1 and 1*prime(1)+2*prime(2)+3*prime(3) = 1*2+2*3+3*15 = 23 = a(3),
%e n=4: no solution => a(4) = 0,
%e n=5: m=7 and 7*prime(7)+..11*prime(11) = 119+152+207+290+341 = 1109 = a(5).
%t Table[If[# == 0, 0, Sum[k Prime@ k, {k, #, n + # - 1}]] &@(SelectFirst[Range[10^3], PrimeQ@ Sum[k Prime@ k, {k, #, n + # - 1}] &] /. x_ /; MissingQ@ x -> 0), {n, 50}] (* _Michael De Vlieger_, Feb 05 2016, Version 10.2 *)
%Y Cf. A000040, A033286, A105455, A268465, A105454, A152117, A119487.
%K nonn
%O 1,1
%A _Zak Seidov_, Feb 05 2016
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