A161666 Smallest of 4 consecutive composite numbers which sum up to prime.

22, 46, 64, 76, 82, 94, 112, 124, 160, 166, 208, 220, 232, 250, 256, 274, 304, 328, 370, 376, 394, 400, 442, 448, 454, 466, 502, 592, 604, 610, 646, 652, 670, 676, 724, 730, 748, 754, 760, 838, 850, 862, 904, 916, 940, 946, 964, 970, 1012, 1066, 1108, 1114

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jun 15 2009

Keywords

• nonn

Comments

One of a(n)+1, a(n)+2, or a(n)+3 is prime, else the sum is even. Therefore there are O(n/log n) members of this sequence up to n by the Prime Number Theorem.

Examples

			22+24+25+26=97,..
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

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]]];If[ !PrimeQ[n]&&PrimeQ[p],AppendTo[lst,n]],{n,2,5*6!}];lst
Transpose[Select[Partition[Select[Range[2000],CompositeQ],4,1],PrimeQ[ Total[ #]]&]] [[1]] (* Harvey P. Dale, Jun 22 2016 *)

Extensions

Comment from Charles R Greathouse IV, Oct 12 2009