# R/Frugal.R In kisungyou/Zseq: Integer Sequence Generator

#### Documented in Frugal

#' Frugal numbers
#'
#' Under OEIS \href{https://oeis.org/A046759}{A046759}, a \emph{Frugal} number has more digits
#' than the number of digits in its prime factorization including exponents. First 6 Frugal numbers are  	125, 128, 243, 256, 343, 512. Though
#' it doesn't matter which base we use, here we adopt only a base of 10.
#'
#' @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 5 Frugal numbers
#' print(Frugal(5))
#'
#' @rdname A046759
#' @aliases A046759 Economical
#' @export
Frugal <- 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(125)
if (n>1){
tgt = as.bigz(126)
iter = 1
while (iter<n){
tgt = tgt + 1
if (is.Frugal(tgt)){
iter = iter+1
output[iter] = tgt
}
}
}

## Rmpfr
if (!gmp){
output = as.integer(output)
}
return(output)
}

#' @keywords internal
#' @noRd
is.Frugal <- function(tgt){
doriginal = countdigit_bigz(tgt)

# 2. prime factorization
pfactor = gmp_primefactorization(tgt)
primes  = pfactor$primes counts = pfactor$multiplicity

dfactored = sum(unlist(lapply(primes, countdigit_bigz)))+sum(unlist(lapply(counts, countdigit_bigz)))

if (doriginal > dfactored){
return(TRUE)
} else {
return(FALSE)
}
}

kisungyou/Zseq documentation built on Feb. 4, 2018, 12:02 a.m.