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A151745 Composites that are the sum of two, three, four and five consecutive composite numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
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

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Last modified April 13 09:02 EDT 2024. Contains 371638 sequences. (Running on oeis4.)