Esthetic numbers: Difference between revisions

=={{header|jq}}==

'''Adapted from [[#Wren|Wren]]'''

{{works with|jq}}

'''Also works with gojq, the Go implementation of jq.'''

<syntaxhighlight lang="jq">

### Preliminaries

# _nwise/1 is included here for the sake of gojq:

def _nwise($n):

def n: if length <= $n then . else .[0:$n] , (.[$n:] | n) end;

n;

def tobase($b):

def digit: "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"[.:.+1];

def mod: . % $b;

def div: ((. - mod) / $b);

def digits: recurse( select(. > 0) | div) | mod ;

# For jq it would be wise to protect against `infinite` as input, but using `isinfinite` confuses gojq

select( (tostring|test("^[0-9]+$")) and 2 <= $b and $b <= 36)

| if . == 0 then "0"

else [digits | digit] | reverse[1:] | add

end;

### Esthetic Numbers

def isEsthetic($b):

if . == 0 then false

else {i: (. % $b), n: ((./$b)|floor) }

| until (.n <= 0 or .emit != null;

(.n % $b) as $j

| if (.i - $j)|length != 1 # abs

then .emit = false

else .n |= ((./$b)|floor)

| .i = $j

end)

| if .emit != null then .emit else true end

end;

# input: {esths}

def dfs($n; $m; $i):

if ($i >= $n and $i <= $m) then .esths += [$i] else . end

| if ($i == 0 or $i > $m) then .

else ($i % 10) as $d

| ($i*10 + $d - 1) as $i1

| ($i1 + 2) as $i2

| if $d == 0

then dfs($n; $m; $i2)

elif $d == 9

then dfs($n; $m; $i1)

else dfs($n; $m; $i1) | dfs($n; $m; $i2)

end

end;

### The tasks

def listEsths(n; n2; m; m2; $perLine; $all):

( {esths: []}

| reduce range(0;10) as $i (.; dfs(n2; m2; $i) )

| "Base 10: \(.esths|length) esthetic numbers between \(n) and \(m)",

if $all

then .esths | _nwise($perLine) | join(" ")

else

(.esths[:$perLine] | join(" ")),

"............",

(.esths[-$perLine:] | join(" "))

end ),

"";

def task($maxBase):

range (2; 1+$maxBase) as $b

| "Base \($b): \(4*$b)th to \(6*$b)th esthetic numbers:",

( [{ n: 1, c: 0 }

| while (.c <= 6*$b;

.emit = null

| if (.n|isEsthetic($b))

then .c += 1

| if .c >= 4*$b

then .emit = "\(.n | tobase($b))"

else .

end

else .

end

| .n += 1 )

| select(.emit).emit]

| _nwise(10) | join(" ") ),

"" ;

task(16),

# the following all use the obvious range limitations for the numbers in question

listEsths(1000; 1010; 9999; 9898; 16; true),

listEsths(1e8; 101010101; 13*1e7; 123456789; 9; true),

listEsths(1e11; 101010101010; 13*1e10; 123456789898; 7; false),

listEsths(1e14; 101010101010101; 13*1e13; 123456789898989; 5; false)

</syntaxhighlight>

{{output}}

(scrollable)

<pre style="height:20lh;overflow:auto">

Base 2: 8th to 12th esthetic numbers:

10101010 101010101 1010101010 10101010101 101010101010

Base 3: 12th to 18th esthetic numbers:

1210 1212 2101 2121 10101 10121 12101

Base 4: 16th to 24th esthetic numbers:

323 1010 1012 1210 1212 1232 2101 2121 2123

Base 5: 20th to 30th esthetic numbers:

323 343 432 434 1010 1012 1210 1212 1232 1234

2101

Base 6: 24th to 36th esthetic numbers:

343 345 432 434 454 543 545 1010 1012 1210

1212 1232 1234

Base 7: 28th to 42th esthetic numbers:

345 432 434 454 456 543 545 565 654 656

1010 1012 1210 1212 1232

Base 8: 32th to 48th esthetic numbers:

432 434 454 456 543 545 565 567 654 656

676 765 767 1010 1012 1210 1212

Base 9: 36th to 54th esthetic numbers:

434 454 456 543 545 565 567 654 656 676

678 765 767 787 876 878 1010 1012 1210

Base 10: 40th to 60th esthetic numbers:

454 456 543 545 565 567 654 656 676 678

765 767 787 789 876 878 898 987 989 1010

1012

Base 11: 44th to 66th esthetic numbers:

456 543 545 565 567 654 656 676 678 765

767 787 789 876 878 898 89A 987 989 9A9

A98 A9A 1010

Base 12: 48th to 72th esthetic numbers:

543 545 565 567 654 656 676 678 765 767

787 789 876 878 898 89A 987 989 9A9 9AB

A98 A9A ABA BA9 BAB

Base 13: 52th to 78th esthetic numbers:

545 565 567 654 656 676 678 765 767 787

789 876 878 898 89A 987 989 9A9 9AB A98

A9A ABA ABC BA9 BAB BCB CBA

Base 14: 56th to 84th esthetic numbers:

565 567 654 656 676 678 765 767 787 789

876 878 898 89A 987 989 9A9 9AB A98 A9A

ABA ABC BA9 BAB BCB BCD CBA CBC CDC

Base 15: 60th to 90th esthetic numbers:

567 654 656 676 678 765 767 787 789 876

878 898 89A 987 989 9A9 9AB A98 A9A ABA

ABC BA9 BAB BCB BCD CBA CBC CDC CDE DCB

DCD

Base 16: 64th to 96th esthetic numbers:

654 656 676 678 765 767 787 789 876 878

898 89A 987 989 9A9 9AB A98 A9A ABA ABC

BA9 BAB BCB BCD CBA CBC CDC CDE DCB DCD

DED DEF EDC

Base 10: 61 esthetic numbers between 1000 and 9999

1010 1012 1210 1212 1232 1234 2101 2121 2123 2321 2323 2343 2345 3210 3212 3232

3234 3432 3434 3454 3456 4321 4323 4343 4345 4543 4545 4565 4567 5432 5434 5454

5456 5654 5656 5676 5678 6543 6545 6565 6567 6765 6767 6787 6789 7654 7656 7676

7678 7876 7878 7898 8765 8767 8787 8789 8987 8989 9876 9878 9898

Base 10: 126 esthetic numbers between 100000000 and 130000000

101010101 101010121 101010123 101012101 101012121 101012123 101012321 101012323 101012343

101012345 101210101 101210121 101210123 101212101 101212121 101212123 101212321 101212323

101212343 101212345 101232101 101232121 101232123 101232321 101232323 101232343 101232345

101234321 101234323 101234343 101234345 101234543 101234545 101234565 101234567 121010101

121010121 121010123 121012101 121012121 121012123 121012321 121012323 121012343 121012345

121210101 121210121 121210123 121212101 121212121 121212123 121212321 121212323 121212343

121212345 121232101 121232121 121232123 121232321 121232323 121232343 121232345 121234321

121234323 121234343 121234345 121234543 121234545 121234565 121234567 123210101 123210121

123210123 123212101 123212121 123212123 123212321 123212323 123212343 123212345 123232101

123232121 123232123 123232321 123232323 123232343 123232345 123234321 123234323 123234343

123234345 123234543 123234545 123234565 123234567 123432101 123432121 123432123 123432321

123432323 123432343 123432345 123434321 123434323 123434343 123434345 123434543 123434545

123434565 123434567 123454321 123454323 123454343 123454345 123454543 123454545 123454565

123454567 123456543 123456545 123456565 123456567 123456765 123456767 123456787 123456789

Base 10: 911 esthetic numbers between 100000000000 and 130000000000

101010101010 101010101012 101010101210 101010101212 101010101232 101010101234 101010121010

............

123456787678 123456787876 123456787878 123456787898 123456789876 123456789878 123456789898

Base 10: 6225 esthetic numbers between 100000000000000 and 130000000000000

101010101010101 101010101010121 101010101010123 101010101012101 101010101012121

............

123456789898767 123456789898787 123456789898789 123456789898987 123456789898989

</pre>