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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 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

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