A065859 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

EXAMPLE

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

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 *)

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=prime(n)%Composite(n); write("b065859.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 01 2009

CROSSREFS

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

Sequence in context: A134690 A295868 A228355 * A258062 A117819 A074461

Adjacent sequences: A065856 A065857 A065858 * A065860 A065861 A065862

KEYWORD

nonn

AUTHOR

Labos Elemer, Nov 26 2001

STATUS

approved