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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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1
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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
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OFFSET
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1,1
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COMMENTS
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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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LINKS
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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[ # ] - # ] &] (* Robert G. Wilson v, Dec 11 2004 *)
Reap[For[n = 4; p = 1, n <= 1500, n++, If[! PrimeQ[n], If[PrimeQ[p] && PrimeQ[n-p], Sow[n]]; p++]]] [[2, 1]] (* Jean-François Alcover, Jul 18 2013 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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