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Search: id:A161667
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| A161667 |
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Smallest of 5 consecutive composite numbers which sum up to prime. |
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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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).
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EXAMPLE
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4+6+8+9+10=37,.. p=37,53,67,83,97,157,..(A060330)
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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]]]+CompositeNext[CompositeNext[CompositeNext[CompositeNext[n\ ]]]]; If[ !PrimeQ[n]&&PrimeQ[p], AppendTo[lst, n]], {n, 2, 5*6!}]; lst
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CROSSREFS
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Cf. A060329, A060330, A161666
Sequence in context: A092292 A157695 A099861 this_sequence A063087 A120064 A028873
Adjacent sequences: A161664 A161665 A161666 this_sequence A161668 A161669 A161670
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KEYWORD
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nonn,new
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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), Nov 11 2009
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