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%I #34 Jun 27 2021 12:39:13
%S -2,-3,-3,-2,1,1,3,4,7,11,11,16,19,19,22,27,32,33,37,39,40,45,48,53,
%T 59,62,63,65,65,68,81,83,88,89,98,99,103,108,111,116,121,121,129,130,
%U 133,134,145,155,158,159,161,165,166,175,180,185,189,190,195,197,198,207
%N n-th prime - n-th composite.
%C 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
%H Reinhard Zumkeller, <a href="/A038529/b038529.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000040(n) - A002808(n). - _Reinhard Zumkeller_, Apr 30 2014
%t 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 *)
%t 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 *)
%o (Haskell)
%o a038529 n = a000040 n - a002808 n -- _Reinhard Zumkeller_, Apr 30 2014
%o (Python)
%o from sympy import prime, composite
%o def A038529(n):
%o return prime(n)-composite(n) # _Chai Wah Wu_, Dec 27 2018
%Y Cf. A014237, A067563.
%K sign,easy
%O 1,1
%A Vasiliy Danilov (danilovv(AT)usa.net), Jul 14 1998
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