Wasteful, equidigital and frugal numbers: Difference between revisions

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(Created Nim solution.)
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First 50: {125,128,243,256,343,512,625,729,1024,1029,1215,1250,1280,1331,1369,1458,1536,1681,1701,1715,1792,1849,1875,2048,2187,2197,2209,2401,2560,2809,3125,3481,3584,3645,3721,4096,4374,4375,4489,4802,4913,5041,5103,5329,6241,6250,6561,6859,6889,7203}
First 50: {125,128,243,256,343,512,625,729,1024,1029,1215,1250,1280,1331,1369,1458,1536,1681,1701,1715,1792,1849,1875,2048,2187,2197,2209,2401,2560,2809,3125,3481,3584,3645,3721,4096,4374,4375,4489,4802,4913,5041,5103,5329,6241,6250,6561,6859,6889,7203}
Below 10^6: 3123</pre>
Below 10^6: 3123</pre>

=={{header|Nim}}==
<syntaxhighlight lang="Nim">import std/[sequtils, strformat, tables]

# Sieve to find the decomposition in prime factors.
const N = 2_700_000
var factors: array[1..N, CountTable[int]]
factors[1].inc(1)

for n in 2..N:
if factors[n].len == 0: # "n" is prime.
var m = n # Powers of "n"
while m <= N:
for k in countup(m, N, m):
factors[k].inc(n)
m *= n

type Category {.pure.} = enum Wasteful = "wasteful"
Equidigital = "equidigital"
Frugal = "frugal"

func digitCount(n, base: Positive): int =
## Return the number of digits of the representation of "n" in given base.
var n = n.Natural
while n != 0:
inc result
n = n div base

proc d(n, base: Positive): int =
## Compute "D(n)" in given base.
for (p, e) in factors[n].pairs:
inc result, p.digitCount(base)
if e > 1: inc result, e.digitCount(base)

proc category(n, base: Positive): Category =
## Return the category of "n" in given base.
let i = n.digitCount(base)
let d = d(n, base)
result = if i < d: Wasteful elif i > d: Frugal else: Equidigital


const N1 = 50
const N2 = 10_000
const Limit = 1_000_000

for base in [10, 11]:

var counts1: array[Category, int] # Total counts.
var counts2: array[Category, int] # Counts for n < Limit.
var numbers1: array[Category, array[1..N1, int]] # First N1 numbers in each category.
var numbers2: array[Category, int] # Number at position N2 in each category.

echo &"For base {base}."
echo "===========\n"
var n = 1
while true:
if n == Limit:
counts2 = counts1
let cat = n.category(base)
inc counts1[cat]
let c = counts1[cat]
if c <= N1:
numbers1[cat][c] = n
elif c == N2:
numbers2[cat] = n
inc n
if allIt(counts1, it >= N2) and n >= Limit: break

for cat in Category.low..Category.high:
echo &"First {N1} {cat} numbers:"
for i, n in numbers1[cat]:
stdout.write &"{n:4}"
stdout.write if i mod 10 == 0: '\n' else: ' '
echo &"\nThe {N2}th {cat} number is {numbers2[cat]}.\n"

echo &"Among numbers less than {Limit}, there are:"
for cat in Category.low..Category.high:
echo &"- {counts2[cat]} {cat} numbers."
echo '\n'
</syntaxhighlight>

{{out}}
<pre>For base 10.
===========

First 50 wasteful numbers:
4 6 8 9 12 18 20 22 24 26
28 30 33 34 36 38 39 40 42 44
45 46 48 50 51 52 54 55 56 57
58 60 62 63 65 66 68 69 70 72
74 75 76 77 78 80 82 84 85 86

The 10000th wasteful number is 14346.

First 50 equidigital numbers:
1 2 3 5 7 10 11 13 14 15
16 17 19 21 23 25 27 29 31 32
35 37 41 43 47 49 53 59 61 64
67 71 73 79 81 83 89 97 101 103
105 106 107 109 111 112 113 115 118 119

The 10000th equidigital number is 33769.

First 50 frugal numbers:
125 128 243 256 343 512 625 729 1024 1029
1215 1250 1280 1331 1369 1458 1536 1681 1701 1715
1792 1849 1875 2048 2187 2197 2209 2401 2560 2809
3125 3481 3584 3645 3721 4096 4374 4375 4489 4802
4913 5041 5103 5329 6241 6250 6561 6859 6889 7203

The 10000th frugal number is 1953125.

Among numbers less than 1000000, there are:
- 831231 wasteful numbers.
- 165645 equidigital numbers.
- 3123 frugal numbers.


For base 11.
===========

First 50 wasteful numbers:
4 6 8 9 10 12 18 20 22 24
26 28 30 33 34 36 38 39 40 42
44 45 46 48 50 51 52 54 55 56
57 58 60 62 63 65 66 68 69 70
72 74 75 76 77 78 80 82 84 85

The 10000th wasteful number is 12890.

First 50 equidigital numbers:
1 2 3 5 7 11 13 14 15 16
17 19 21 23 25 27 29 31 32 35
37 41 43 47 49 53 59 61 64 67
71 73 79 81 83 89 97 101 103 107
109 113 121 122 123 127 129 131 133 134

The 10000th equidigital number is 33203.

First 50 frugal numbers:
125 128 243 256 343 512 625 729 1024 1331
1369 1458 1536 1681 1701 1715 1792 1849 1875 2048
2187 2197 2209 2401 2560 2809 3072 3125 3481 3584
3645 3721 4096 4374 4375 4489 4802 4913 5041 5103
5120 5329 6241 6250 6561 6859 6889 7168 7203 7921

The 10000th frugal number is 2659171.

Among numbers less than 1000000, there are:
- 795861 wasteful numbers.
- 200710 equidigital numbers.
- 3428 frugal numbers.</pre>


=={{header|Perl}}==
=={{header|Perl}}==
Retrieved from "https://rosettacode.org/wiki/Wasteful,_equidigital_and_frugal_numbers"