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#' Regular numbers
#'
#' Under OEIS \href{https://oeis.org/A051037}{A051037}, a \emph{Regular} number - also known as 5-smooth - is a positive integer that
#' even divide powers of 60, or equivalently, whose prime divisors are only 2,3, and 5. First 6 Regular numbers are 1, 2, 3, 4, 5, 6.
#'
#' @param n the number of first \code{n} entries from the sequence.
#' @param gmp a logical; \code{TRUE} to use large number representation, \code{FALSE} otherwise.
#'
#' @return a vector of length \code{n} containing first entries from the sequence.
#'
#' @examples
#' ## generate first 20 Regular numbers
#' print(Regular(20))
#'
#' @rdname A051037
#' @aliases A051037
#' @export
Regular <- function(n, gmp=TRUE){
## Preprocessing for 'n'
n = check_n(n)
## Main Computation : first, compute in Rmpfr form
output = as.bigz(numeric(n))
output[1] = as.bigz(1)
if (n>1){
tgt = as.bigz(1)
iter = 1
while (iter<n){
tgt = tgt + 1
if (is.Regular(tgt)){
iter = iter+1
output[iter] = tgt
}
}
}
## Rmpfr
if (!gmp){
output = as.integer(output)
}
return(output)
}
#' @keywords internal
#' @noRd
is.Regular <- function(n){
pdivs = as.integer(gmp_divisors_prime(n))
tgtps = as.integer(c(2,3,5))
if (length(pdivs)<3){
return(all(pdivs%in%tgtps))
} else if (length(pdivs)==3){
if (all(sort(pdivs)==sort(tgtps))){
return(TRUE)
} else {
return(FALSE)
}
} else {
return(FALSE)
}
}
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