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 A065859 Remainder when the n-th prime is divided by the n-th composite number. 2
 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

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Last modified July 25 09:49 EDT 2021. Contains 346289 sequences. (Running on oeis4.)