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

1,1

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.

Links

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

Example

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

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 *)

Crossrefs

Sequence in context: A281187 A335297 A158862 * A132763 A250723 A044099

Adjacent sequences: A161663 A161664 A161665 * A161667 A161668 A161669

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jun 15 2009

Extensions

Comment from Charles R Greathouse IV, Oct 12 2009

Status

approved