Integers that describe their own digits

self_described_digits.R

# Integers that describe their own digits
# Nathan Stephens
# 3/28/2023

###################
# Background
###################
# We seek numbers whose digits describe how many digits are in that same number
# For example, consider 42,101,000, which has 8 digits. 
# We index those digits 0-7, and consider how many of each index are in the number.
# There are four 0's
# There are two 1's
# There is one 3
# And there is one 4
###################

###################
# Solutions
###################
#  4:          1210
#  4:          2020
#  5:         21200
#  6:          #N/A
#  7:       3211000
#  8:      42101000
#  9:     521001000
# 10:    6210001000
# 11:   72100001000
# 12:  821000001000
# 13: 9210000001000
###################

# Input size
n<-7
s<-0:(n-1)

# Prune permutation inputs
prune<-as.list(as.data.frame(matrix(s, n, n)))
prune[length(prune)]<-0L
prune<-lapply(prune, function(x) head(x, n-3))

# Create permutations and prune
M<-expand.grid(prune)
M<-M[apply(M, 1, sum)==n, ]

# Identify results
f<-function(x, s) all(sort(x)==rep(s, x))
ind<-which(apply(M, 1, f, s))
out<-as.numeric(apply(M[ind, ], 1, paste, collapse=""))
out

###################
# Alternative code
###################
s<--1+1:7
M<-expand.grid(as.data.frame(matrix(s, length(s), length(s))))
M[which(apply(M, 1, function(x) all(sort(x)==rep(s, x)))), ]

The alternative code calculates results in three lines, but there is no pruning, so computations are slow.