A151745 Composites that are the sum of two, three, four and five consecutive composite numbers.

405, 1395, 3435, 3525, 4245, 4365, 6675, 6885, 7155, 7515, 7995, 8325, 8445, 9075, 10365, 10845, 11205, 11543, 13005, 14235, 14325, 18075, 19725, 19875, 22605, 23257, 23475, 23617, 26805, 27315, 29835, 29955, 31035, 32355, 32925, 33165, 34395

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..6214

Formula

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

Example

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).

Maple

N:= 10^5: # for terms <= N
Comps:= remove(isprime, [$2..N]):
PSComps:= [0, op(ListTools:-PartialSums(Comps))]:
C2:= convert(PSComps[3..-1]-PSComps[1..-3], set):
C3:= convert(PSComps[4..-1]-PSComps[1..-4], set):
C4:= convert(PSComps[5..-1]-PSComps[1..-5], set):
C5:= convert(PSComps[6..-1]-PSComps[1..-6], set):
R:= convert(Comps, set) intersect C2 intersect C3 intersect C4 intersect C5:
sort(convert(R, list)); # Robert Israel, Aug 17 2020

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 *)

Crossrefs

Sequence in context: A337047 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

Corrected by Robert Israel, Aug 17 2020

Status

approved