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

1,3

Links

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

Formula

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

Example

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

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 *)

Prog

(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=Composite(n)%n; write("b065860.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 02 2009

Crossrefs

Cf. A002808, A065855-A065864.

Sequence in context: A212868 A184616 A261139 * A363494 A010110 A116905

Adjacent sequences: A065857 A065858 A065859 * A065861 A065862 A065863

Keyword

nonn

Author

Labos Elemer, Nov 26 2001

Status

approved