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A151745
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Composites that are the sum of two, three, four and five consecutive composite numbers.
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4
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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
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..6214
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FORMULA
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Intersection of A151740, A151741, A151742 and A151743. - R. J. Mathar, Jun 17 2009
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EXAMPLE
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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).
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MAPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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Sequence in context: A337047 A169904 A267893 * A204636 A224527 A219147
Adjacent sequences: A151742 A151743 A151744 * A151746 A151747 A151748
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KEYWORD
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nonn
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AUTHOR
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Claudio Meller, Jun 15 2009
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EXTENSIONS
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Corrected and extended by Harvey P. Dale, Nov 25 2014
Corrected by Robert Israel, Aug 17 2020
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STATUS
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approved
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