A065860 Remainder when the n-th composite number is divided by n.

0, 0, 2, 1, 0, 0, 0, 7, 7, 8, 9, 9, 9, 10, 10, 10, 10, 10, 11, 12, 12, 12, 12, 12, 13, 13, 13, 14, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 19, 19, 19, 19, 19, 20, 20, 20, 21, 22, 22, 22, 22, 22, 23, 23, 23, 24, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 25, 26, 26

Offset: 1

Author

Labos Elemer, Nov 26 2001

Keywords

• nonn

Examples

			n=100, c(100)=133, a(100)=33.
		

Links

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

Crossrefs

Cf. A002808, A065855-A065864.

Programs

Mathematica

Module[{nn=100,cmps,len},cmps=Select[Range[nn],CompositeQ];len=Length[ cmps]; Mod[#[[1]],#[[2]]]&/@Thread[{cmps,Range[len]}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 29 2020 *)

PARI

Composite(n) = { my(k=n + primepi(n) + 1); while (k != n + primepi(k) + 1, k = n + primepi(k) + 1); k }
a(n) = { Composite(n)%n } \\ Harry J. Smith, Nov 02 2009

Formula

a(n) = A002808(n) mod n.