A151744 Primes which are the sum of two, three, four and five consecutive composite numbers.

17783, 25057, 47303, 48383, 49297, 76343, 89783, 205703, 412343, 516457, 704183, 754417, 790703, 938183, 1105343, 1110743, 1279583, 1563503, 1632817, 1744583, 1890743, 1903103, 2062943, 2276303, 2714617, 2802383, 2812897, 2932703

Offset: 1

Author

Claudio Meller, Jun 15 2009

Keywords

• nonn

Comments

17783 is in the list because: 17783 = 8891 + 8892 (sum of two consecutive composite numbers)

17783 = 5926 + 5928 + 5929 (sum of three consecutive composite numbers)

17783 = 4444 + 4445 + 4446 + 4448 (sum of four consecutive composite numbers)

17783 = 3554 + 3555 + 3556 + 3558 + 3560 (sum of five consecutive composite numbers)

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..100

Programs

Mathematica

CompositeNext[n_]:=Module[{k=n+1},While[PrimeQ[k],k++ ];k]; q=9!; 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 *)
Module[{comps=Select[Range[2*10^6],CompositeQ]},Intersection@@ Table[ Select[ Total/@ Partition[comps,n,1],PrimeQ],{n,2,5}]] (* Harvey P. Dale, Apr 16 2015 *)

Formula

Intersection of A060254, A060328, A060329 and A060330. - R. J. Mathar, Jun 17 2009

Extensions

Extended beyond a(7) by Klaus Brockhaus, Jun 16 2009