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%I #21 Jan 03 2021 00:34:32
%S 3,5,7,5,5,7,7,7,5,5,7,13,11,7,7,7,11,11,13,13,7,7,7,11,11,11,17,11,
%T 13,13,13,19,13,13,11,11,11,23,11,13,17,13,13,13,19,13,13,19,17,19,19,
%U 19,29,23,23,17,11,11,11,17,11,13,17,17,19,23,19,13,13,13
%N a(n) is the smallest prime such that 2n=p1+p2*p3 where Max(p1,p2,p3)=a(n) and p1, p2 p3 are odd primes.
%C a(n) is defined for integers n >= 6.
%H Lei Zhou, <a href="/A238205/b238205.txt">Table of n, a(n) for n = 6..10000</a>
%e n=6, 2n=12=3+3*3, Max[3,3,3]=3, so a(6)=3;
%e n=7, 2n=12=5+3*3, Max[5,3,3]=5, so a(7)=5;
%e ..
%e n=10, 2n=20=11+3*3=5+5*3, Max[11,3,3]=11, Max[5,5,3]=5, Min[11,5]=5, so a(10)=5.
%t Table[p = 2; r = n; While[p = NextPrime[p]; m = n - p; m >= 9, f = Transpose[FactorInteger[m]]; If[(Total[f[[2]]] == 2)&&(f[[1,1]]>2), s = Max[Max[f[[1]]], p]; If[r > s, r = s]]]; r, {n, 12, 150, 2}]
%Y Cf. A002375.
%K nonn,easy
%O 6,1
%A _Lei Zhou_, Feb 20 2014
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