

A151745


Composites that are the sum of two, three, four and five consecutive composite numbers.


3



405, 1395, 3435, 3525, 4245, 4365, 6675, 6885, 7155, 7515, 7995, 8325, 8445, 9075, 10365, 10845, 11205, 11543, 13005, 14235, 14325, 17783, 18075, 19725, 19875, 22605, 23257, 23475, 23617, 25057, 26805, 27315, 29835, 29955, 31035, 32355, 32925, 33165, 34395
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

405 is in the list because it is composite and
405 = 202 + 203 (Sum of two consecutive composite numbers)
405 = 134 + 135 + 136 (Sum of three consecutive composite numbers)
405 = 99 + 100 + 102 + 104 (Sum of four consecutive composite numbers)
405 = 78 + 80 + 81 + 82 + 84 (Sum of five consecutive composite numbers).


LINKS

Table of n, a(n) for n=1..39.


FORMULA

Intersection of A151740, A151741, A151742 and A151743.  R. J. Mathar, Jun 17 2009


MATHEMATICA

CompositeNext[n_]:=Module[{k=n+1}, While[PrimeQ[k], k++ ]; k]; q=8!; 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 *)
With[{c=Select[Range[20000], CompositeQ]}, Intersection[Total/@Partition[ c, 2, 1], Total/@Partition[c, 3, 1], Total/@Partition[c, 4, 1], Total/@ Partition[c, 5, 1]]] (* Harvey P. Dale, Nov 25 2014 *)


CROSSREFS

Sequence in context: A198536 A169904 A267893 * A204636 A224527 A219147
Adjacent sequences: A151742 A151743 A151744 * A151746 A151747 A151748


KEYWORD

nonn


AUTHOR

Claudio Meller, Jun 15 2009


EXTENSIONS

Corrected and extended by Harvey P. Dale, Nov 25 2014


STATUS

approved



