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
Keywords
Examples
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
- Robert Israel, Table of n, a(n) for n = 1..6214
Programs
-
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 *)
Formula
Extensions
Corrected and extended by Harvey P. Dale, Nov 25 2014
Corrected by Robert Israel, Aug 17 2020