OFFSET
1,1
COMMENTS
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.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
EXAMPLE
22+24+25+26=97,..
MATHEMATICA
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
Transpose[Select[Partition[Select[Range[2000], CompositeQ], 4, 1], PrimeQ[ Total[ #]]&]] [[1]] (* Harvey P. Dale, Jun 22 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Jun 15 2009
EXTENSIONS
Comment from Charles R Greathouse IV, Oct 12 2009
STATUS
approved