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Search: id:A100718
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| A100718 |
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Composite numbers C(p) such that p and C(p)-p are primes. |
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+0
2
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| 8, 10, 14, 30, 54, 58, 62, 66, 82, 108, 114, 120, 178, 182, 204, 210, 318, 324, 330, 352, 366, 430, 506, 544, 560, 586, 596, 616, 704, 738, 792, 858, 870, 914, 918, 960, 988, 990, 1026, 1030, 1062, 1164, 1170, 1194, 1404, 1442, 1446, 1462, 1464, 1470, 1498
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Nextprime(C(n))=P(C(n)-n)=(C(n)-n)-th prime.
A proof that the sequence is infinite would be nice.
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FORMULA
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C(n)=n+k where k is such that nextprime(C(n))=k-th prime.
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EXAMPLE
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a(4)=30 because C(19)=30=19+11, 19 and 11 are prime and P(11)=31=nextprime(30)
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MATHEMATICA
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Composite[n_Integer] := FixedPoint[n + PrimePi[ # ] + 1 &, n]; Composite /@ Select[ Prime[ Range[ 205]], PrimeQ[ Composite[ # ] - # ] &] (from Robert G. Wilson v Dec 11 2004)
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CROSSREFS
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Sequence in context: A087695 A134321 A027693 this_sequence A063190 A101763 A154568
Adjacent sequences: A100715 A100716 A100717 this_sequence A100719 A100720 A100721
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KEYWORD
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nonn
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AUTHOR
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Robin Garcia (verob99(AT)teleline.es), Dec 11 2004
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 11 2004
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