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

#### Documented in Equidigital

#' Equidigital numbers
#'
#' Under OEIS \href{https://oeis.org/A046758}{A046758}, an \emph{Equidigital} number has equal digits
#' as the number of digits in its prime factorization including exponents. First 6 Equidigital numbers are 1, 2, 3, 5, 7, 10. 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 20 Equidigital numbers
#' print(Equidigital(20))
#'
#' @rdname A046758
#' @aliases A046758
#' @export
Equidigital <- 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.Equidigital(tgt)){
iter = iter+1
output[iter] = tgt
}
}
}

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

#' @keywords internal
#' @noRd
is.Equidigital <- function(tgt){
# 1. original digits
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)))

#
# dfactored = 0
# for (i in 1:length(pfactor$primes)){ # dfactored = dfactored + floor(log10(pfactor$primes[i]))+1
#   if (pfactor$multiplicity[i]!=1){ # dfactored = dfactored + floor(log10(pfactor$multiplicity[i]))+1
#   }
# }

if (doriginal==dfactored){
return(TRUE)
} else {
return(FALSE)
}
}
countdigit_bigz <- function(x){
if (!is.bigz(x)){
x = as.bigz(x)
}
if (x==1){
return(0)
} else {
return(length(unlist(strsplit(as.character(x),""))))
}
}

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