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Search: id:A161666
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| A161666 |
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Smallest of 4 consecutive composite numbers which sum up to prime. |
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+0
2
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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.
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EXAMPLE
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22+24+25+26=97,..
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MATHEMATICA
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CompositeNext[n_]:=Module[{k=n+1}, While[PrimeQ[k], k++ ]; k]; lst={}; Do[p=n+CompositeNext[n]+CompositeNext[CompositeNext[n]]+CompositeNext[CompositeN\ ext[CompositeNext[n]]]; If[ !PrimeQ[n]&&PrimeQ[p], AppendTo[lst, n]], {n, 2, 5*6!}]; lst
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CROSSREFS
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Sequence in context: A041966 A106838 A158862 this_sequence A132763 A044099 A044480
Adjacent sequences: A161663 A161664 A161665 this_sequence A161667 A161668 A161669
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KEYWORD
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nonn
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 15 2009
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EXTENSIONS
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Comment by Charles R Greathouse IV (charles.greathouse(AT)case.edu), Oct 12 2009
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