A161667 Smallest of 5 consecutive composite numbers which sum up to prime.

4, 8, 10, 14, 16, 28, 56, 58, 68, 70, 98, 106, 134, 146, 148, 178, 188, 190, 194, 196, 236, 308, 310, 344, 346, 428, 520, 566, 568, 614, 638, 640, 658, 808, 824, 854, 856, 1018, 1028, 1030, 1058, 1226, 1276, 1318, 1448, 1480, 1484, 1616, 1784, 1876, 1946, 2024

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jun 15 2009

Keywords

• nonn

Comments

There are at most 5n/log n members of this sequence up to n, since at least one of a(n), a(n) + 1, ..., a(n) + 4 is prime (else their sum is divisible by 5).

Examples

			4+6+8+9+10=37,.. p=37,53,67,83,97,157,..(A060330)
		

Crossrefs

Cf. A060329, A060330, A161666

Programs

Mathematica

CompositeNext[n_]:=Module[{k=n+1},While[PrimeQ[k],k++ ];k]; lst={};Do[p=n+CompositeNext[n]+CompositeNext[CompositeNext[n]]+CompositeNext[CompositeNext[CompositeNext[n]]]+CompositeNext[CompositeNext[CompositeNext[CompositeNext[n]]]];If[ !PrimeQ[n]&&PrimeQ[p],AppendTo[lst,n]],{n,2,5*6!}];lst
Transpose[Select[Partition[Select[Range[2100],CompositeQ],5,1],PrimeQ[ Total[ #]]&]][[1]] (* Harvey P. Dale, Aug 14 2014 *)

Extensions

Comment from Charles R Greathouse IV, Nov 11 2009