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%I #14 Jun 17 2018 01:59:36
%S 2,3,5,7,1,1,3,4,7,11,11,16,19,19,22,1,5,5,7,7,7,11,13,17,21,23,23,23,
%T 21,23,35,35,39,39,47,47,49,53,55,2,5,1,5,4,5,4,13,19,20,19,17,17,16,
%U 23,26,29,29,28,31,29,28,35,46,47,43,44,55,58,65,64,65,65,70,73,73,71
%N Remainder when the n-th prime is divided by the n-th composite number.
%H Harry J. Smith, <a href="/A065859/b065859.txt">Table of n, a(n) for n = 1..1000</a>
%e n=100, p(100)=541, c(100)=133, a(100)=9 because 541 = 4*133 + 9.
%t a[n]=Mod[p(n), c(n)]=Mod[A000040(n), A002808(n)]
%t With[{nn=80},Module[{prs=Prime[Range[nn]],comps},comps=Take[Complement[ Range[2,Prime[nn]+1],prs],Length[prs]];Mod[#[[1]],#[[2]]]&/@ Thread[ {prs,comps}]]] (* _Harvey P. Dale_, Apr 18 2012 *)
%o (PARI) Composite(n) = { local(k); k=n + primepi(n) + 1; while (k != n + primepi(k) + 1, k = n + primepi(k) + 1); return(k) } { for (n = 1, 1000, a=prime(n)%Composite(n); write("b065859.txt", n, " ", a) ) } \\ _Harry J. Smith_, Nov 01 2009
%Y Cf. A000040, A002808, A004648, A065133, A065134, A065855-A065864, A065134.
%K nonn
%O 1,1
%A _Labos Elemer_, Nov 26 2001
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