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A161666 Smallest of 4 consecutive composite numbers which sum up to prime. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A190614 A281187 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

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Last modified February 27 06:36 EST 2020. Contains 332299 sequences. (Running on oeis4.)