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A161666 Smallest of 4 consecutive composite numbers which sum up to prime. 2


%S 22,46,64,76,82,94,112,124,160,166,208,220,232,250,256,274,304,328,

%T 370,376,394,400,442,448,454,466,502,592,604,610,646,652,670,676,724,

%U 730,748,754,760,838,850,862,904,916,940,946,964,970,1012,1066,1108,1114

%N Smallest of 4 consecutive composite numbers which sum up to prime.

%C One of a(n)+1, a(n)+2, or a(n)+3 is prime, else the sum is even. Therefore there are O(n/log n) members of this sequence up to n by the Prime Number Theorem.

%H Harvey P. Dale, <a href="/A161666/b161666.txt">Table of n, a(n) for n = 1..1000</a>

%e 22+24+25+26=97,..

%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]]];If[ !PrimeQ[n]&&PrimeQ[p],AppendTo[lst,n]],{n,2,5*6!}];lst

%t Transpose[Select[Partition[Select[Range[2000],CompositeQ],4,1],PrimeQ[ Total[ #]]&]] [[1]] (* _Harvey P. Dale_, Jun 22 2016 *)

%K nonn

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Jun 15 2009

%E Comment from _Charles R Greathouse IV_, Oct 12 2009

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Last modified March 30 06:40 EDT 2020. Contains 333119 sequences. (Running on oeis4.)