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A038529
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n-th prime - n-th composite.
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8
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-2, -3, -3, -2, 1, 1, 3, 4, 7, 11, 11, 16, 19, 19, 22, 27, 32, 33, 37, 39, 40, 45, 48, 53, 59, 62, 63, 65, 65, 68, 81, 83, 88, 89, 98, 99, 103, 108, 111, 116, 121, 121, 129, 130, 133, 134, 145, 155, 158, 159, 161, 165, 166, 175, 180, 185, 189, 190, 195, 197, 198, 207
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OFFSET
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1,1
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COMMENTS
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Sequence is monotonically increasing starting from a(2). a(n) = a(n+1) if and only if both prime(n)+2 and composite(n)+1 are prime. - Jianing Song, Jun 27 2021
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LINKS
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FORMULA
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MATHEMATICA
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composite[n_Integer] := Block[{k=n+PrimePi[n]+1}, While[k-PrimePi[k]-1 != n, k++]; k]; Table[Prime[n] - composite[n], {n, 65}] (* corrected by Harvey P. Dale, Aug 08 2011 *)
Module[{nn=300, prs, cmps, len}, prs=Prime[Range[PrimePi[nn]]]; cmps= Complement[ Range[4, nn], prs]; len=Min[Length[prs], Length[cmps]]; #[[1]]- #[[2]]&/@ Thread[{Take[prs, len], Take[cmps, len]}]] (* Harvey P. Dale, Jun 18 2015 *)
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PROG
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(Haskell)
(Python)
from sympy import prime, composite
return prime(n)-composite(n) # Chai Wah Wu, Dec 27 2018
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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Vasiliy Danilov (danilovv(AT)usa.net), Jul 14 1998
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STATUS
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approved
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