%I A161667
%S A161667 4,8,10,14,16,28,56,58,68,70,98,106,134,146,148,178,188,190,194,196,236,
%T A161667 308,310,344,346,428,520,566,568,614,638,640,658,808,824,854,856,1018,
%U A161667 1028,1030,1058,1226,1276,1318,1448,1480,1484,1616,1784,1876,1946,2024
%N A161667 Smallest of 5 consecutive composite numbers which sum up to prime.
%C A161667 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 A161667 4+6+8+9+10=37,.. p=37,53,67,83,97,157,..(A060330)
%t A161667 CompositeNext[n_]:=Module[{k=n+1},While[PrimeQ[k],k++ ];k]; lst={};Do[p=n+CompositeNext[n]+CompositeNext[Comp\
               ositeNext[n]]+CompositeNext[CompositeNext[CompositeNext[n]]]+CompositeNext[CompositeNext[CompositeNext[Co\
               mpositeNext[n]]]];If[ !PrimeQ[n]&&PrimeQ[p],AppendTo[lst,n]],{n,2,
               5*6!}];lst
%Y A161667 Cf. A060329, A060330, A161666
%Y A161667 Sequence in context: A092292 A157695 A099861 this_sequence A063087 A120064 
               A028873
%Y A161667 Adjacent sequences: A161664 A161665 A161666 this_sequence A161668 A161669 
               A161670
%K A161667 nonn,new
%O A161667 1,1
%A A161667 Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 15 2009
%E A161667 Comment by Charles R Greathouse IV (charles.greathouse(AT)case.edu), 
               Nov 11 2009