OFFSET
1,1
COMMENTS
17783 is in the list because: 17783 = 8891 + 8892 (sum of two consecutive composite numbers)
17783 = 5926 + 5928 + 5929 (sum of three consecutive composite numbers)
17783 = 4444 + 4445 + 4446 + 4448 (sum of four consecutive composite numbers)
17783 = 3554 + 3555 + 3556 + 3558 + 3560 (sum of five consecutive composite numbers)
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..100
FORMULA
MATHEMATICA
CompositeNext[n_]:=Module[{k=n+1}, While[PrimeQ[k], k++ ]; k]; q=9!; lst2={}; Do[If[ !PrimeQ[n], c=CompositeNext[n]; a2=n+c; If[PrimeQ[a2], AppendTo[lst2, a2]]], {n, q}]; lst2; lst3={}; Do[If[ !PrimeQ[n], c1=CompositeNext[n]; c2=CompositeNext[c1]; a3=n+c1+c2; If[PrimeQ[a3], AppendTo[lst3, a3]]], {n, q}]; lst3; lst4={}; Do[If[ !PrimeQ[n], c1=CompositeNext[n]; c2=CompositeNext[c1]; c3=CompositeNext[c2]; a4=n+c1+c2+c3; If[PrimeQ[a4], AppendTo[lst4, a4]]], {n, q}]; lst4; lst5={}; Do[If[ !PrimeQ[n], c1=CompositeNext[n]; c2=CompositeNext[c1]; c3=CompositeNext[c2]; c4=CompositeNext[c3]; a5=n+c1+c2+c3+c4; If[PrimeQ[a5], AppendTo[lst5, a5]]], {n, q}]; lst5; Intersection[lst2, lst3, lst4, lst5] (* Vladimir Joseph Stephan Orlovsky, Jun 17 2009 *)
Module[{comps=Select[Range[2*10^6], CompositeQ]}, Intersection@@ Table[ Select[ Total/@ Partition[comps, n, 1], PrimeQ], {n, 2, 5}]] (* Harvey P. Dale, Apr 16 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Claudio Meller, Jun 15 2009
EXTENSIONS
Extended beyond a(7) by Klaus Brockhaus, Jun 16 2009
STATUS
approved