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

1,1

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

Formula

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

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 *)

Crossrefs

Sequence in context: A235023 A133540 A237776 * A250333 A203920 A236649

Adjacent sequences: A151741 A151742 A151743 * A151745 A151746 A151747

Keyword

nonn

Author

Claudio Meller, Jun 15 2009

Extensions

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

Status

approved