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%I #5 Aug 14 2014 18:25:45
%S 4,8,10,14,16,28,56,58,68,70,98,106,134,146,148,178,188,190,194,196,
%T 236,308,310,344,346,428,520,566,568,614,638,640,658,808,824,854,856,
%U 1018,1028,1030,1058,1226,1276,1318,1448,1480,1484,1616,1784,1876,1946,2024
%N Smallest of 5 consecutive composite numbers which sum up to prime.
%C There are at most 5n/log n members of this sequence up to n, since at least one of a(n), a(n) + 1, ..., a(n) + 4 is prime (else their sum is divisible by 5).
%e 4+6+8+9+10=37,.. p=37,53,67,83,97,157,..(A060330)
%t CompositeNext[n_]:=Module[{k=n+1},While[PrimeQ[k],k++ ];k]; lst={};Do[p=n+CompositeNext[n]+CompositeNext[CompositeNext[n]]+CompositeNext[CompositeNext[CompositeNext[n]]]+CompositeNext[CompositeNext[CompositeNext[CompositeNext[n]]]];If[ !PrimeQ[n]&&PrimeQ[p],AppendTo[lst,n]],{n,2,5*6!}];lst
%t Transpose[Select[Partition[Select[Range[2100],CompositeQ],5,1],PrimeQ[ Total[ #]]&]][[1]] (* _Harvey P. Dale_, Aug 14 2014 *)
%Y Cf. A060329, A060330, A161666
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jun 15 2009
%E Comment from _Charles R Greathouse IV_, Nov 11 2009
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