% File src/library/stats/man/nextn.Rd
% Part of the R package, https://www.R-project.org
% Copyright 1995-2018 R Core Team
% Distributed under GPL 2 or later

\name{nextn}
\title{Find Highly Composite Numbers}
\usage{
nextn(n, factors = c(2,3,5))
}
\alias{nextn}
\arguments{
  \item{n}{a vector of integer numbers (of type \code{"integer"}
    \emph{or} \code{"double"}).}
  \item{factors}{a vector of positive integer factors (at least \eqn{2}
    and preferably relative prime, see the note).}
}
\description{
  \code{nextn} returns the smallest integer,
  greater than or equal to \code{n}, which can be obtained
  as a product of powers of the values contained in \code{factors}.

  \code{nextn()} is intended to be used to find a suitable length
  to zero-pad the argument of \code{\link{fft}}
  so that the transform is computed quickly.
  The default value for \code{factors} ensures this.
}
\value{a vector of the same \code{\link{length}} as \code{n}, of type
  \code{"integer"} when the values are small enough (determined before
  computing them) and \code{"double"} otherwise.
}
\note{If the factors in \code{factors} are \emph{not} relative prime,
  i.e., have themselves a common factor larger than one, the result may
  be wrong in the sense that it may not be the \emph{smallest} integer.
  E.g., \code{nextn(91, c(2,6))} returns 128 instead of 96 as
  \code{nextn(91, c(2,3))} returns.

  When the resulting \code{N <- nextn(..)} is larger than \code{2^53}, a
  warning with the true 64-bit integer value is signalled, as integers
  above that range may not be representable in double precision.

  If you really need to deal with such large integers, it may be
  advisable to use package \CRANpkg{gmp}.
}
\seealso{
  \code{\link{convolve}}, \code{\link{fft}}.
}
\examples{
nextn(1001) # 1024
table(nextn(599:630))
n <- 1:100 ; plot(n, nextn(n) - n, type = "o", lwd=2, cex=1/2)
}
\keyword{math}