A065859 Remainder when the n-th prime is divided by the n-th composite number.

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, 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, 23, 26, 29, 29, 28, 31, 29, 28, 35, 46, 47, 43, 44, 55, 58, 65, 64, 65, 65, 70, 73, 73, 71

Offset: 1

Author

Labos Elemer, Nov 26 2001

Keywords

• nonn

Examples

			n=100, p(100)=541, c(100)=133, a(100)=9 because 541 = 4*133 + 9.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A002808, A004648, A065133, A065134, A065855-A065864, A065134.

Programs

Mathematica

a[n]=Mod[p(n), c(n)]=Mod[A000040(n), A002808(n)]
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 *)

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