Esthetic numbers: Difference between revisions
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=={{header|Phix}}== |
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<lang Phix>constant aleph = "0123456789ABCDEF" |
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include builtins\ordinal.e |
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function efill(string s, integer ch, i) |
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s[i] = ch |
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for j=i+1 to length(s) do |
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ch = iff(ch>='1'?iff(ch='A'?'9':ch-1):'1') |
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s[j] = ch |
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end for |
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return s |
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end function |
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function esthetic(string s, integer base = 10) |
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for i=length(s) to 1 by -1 do |
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integer ch = s[i], cp = iff(i>1?s[i-1]:'Z') |
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if i>1 and ch<cp and cp<aleph[base] then |
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ch = iff(ch='8'?'A':iff(ch='9'?'B':ch+2)) |
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return efill(s,ch,i) |
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elsif i=1 and ch<aleph[base] then |
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ch = iff(ch='9'?'A':ch+1) |
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return efill(s,ch,i) |
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end if |
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end for |
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s = "1"&s |
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return efill(s,'1',1) |
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end function |
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string s |
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sequence res |
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for base=2 to 16 do |
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s = "" |
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res = {} |
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for i=1 to base*6 do |
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s = esthetic(s, base) |
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if i>=base*4 then |
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res = append(res,s) |
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end if |
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end for |
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printf(1,"%d%s through %d%s esthetic numbers in base %d\n%s\n", |
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{base*4,ord(base*4),base*6,ord(base*6),base,join_by(res,1,16)}) |
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end for |
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s = efill("1000",'1',1) |
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res = {} |
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while length(s)=4 do |
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res = append(res,s) |
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s = esthetic(s) |
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end while |
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printf(1,"Base 10 esthetic numbers between 1,000 and 9,999:\n%s\n", |
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{join_by(res,1,20)}) |
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s = efill("100000000",'1',1) |
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res = {} |
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while s<"130000000" do |
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res = append(res,s) |
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s = esthetic(s) |
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end while |
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printf(1,"Base 10 esthetic numbers between 100,000,000 and 130,000,000:\n%s\n", |
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{join_by(res,1,9)})</lang> |
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{{out}} |
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<pre> |
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8th through 12th esthetic numbers in base 2 |
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10101010 101010101 1010101010 10101010101 101010101010 |
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12th through 18th esthetic numbers in base 3 |
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1210 1212 2101 2121 10101 10121 12101 |
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16th through 24th esthetic numbers in base 4 |
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323 1010 1012 1210 1212 1232 2101 2121 2123 |
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20th through 30th esthetic numbers in base 5 |
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323 343 432 434 1010 1012 1210 1212 1232 1234 2101 |
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24th through 36th esthetic numbers in base 6 |
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343 345 432 434 454 543 545 1010 1012 1210 1212 1232 1234 |
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28th through 42nd esthetic numbers in base 7 |
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345 432 434 454 456 543 545 565 654 656 1010 1012 1210 1212 1232 |
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32nd through 48th esthetic numbers in base 8 |
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432 434 454 456 543 545 565 567 654 656 676 765 767 1010 1012 1210 |
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1212 |
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36th through 54th esthetic numbers in base 9 |
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434 454 456 543 545 565 567 654 656 676 678 765 767 787 876 878 |
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1010 1012 1210 |
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40th through 60th esthetic numbers in base 10 |
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454 456 543 545 565 567 654 656 676 678 765 767 787 789 876 878 |
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898 987 989 1010 1012 |
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44th through 66th esthetic numbers in base 11 |
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456 543 545 565 567 654 656 676 678 765 767 787 789 876 878 898 |
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89A 987 989 9A9 A98 A9A 1010 |
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48th through 72nd esthetic numbers in base 12 |
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543 545 565 567 654 656 676 678 765 767 787 789 876 878 898 89A |
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987 989 9A9 9AB A98 A9A ABA BA9 BAB |
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52nd through 78th esthetic numbers in base 13 |
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545 565 567 654 656 676 678 765 767 787 789 876 878 898 89A 987 |
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989 9A9 9AB A98 A9A ABA ABC BA9 BAB BCB CBA |
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56th through 84th esthetic numbers in base 14 |
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565 567 654 656 676 678 765 767 787 789 876 878 898 89A 987 989 |
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9A9 9AB A98 A9A ABA ABC BA9 BAB BCB BCD CBA CBC CDC |
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60th through 90th esthetic numbers in base 15 |
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567 654 656 676 678 765 767 787 789 876 878 898 89A 987 989 9A9 |
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9AB A98 A9A ABA ABC BA9 BAB BCB BCD CBA CBC CDC CDE DCB DCD |
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64th through 96th esthetic numbers in base 16 |
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654 656 676 678 765 767 787 789 876 878 898 89A 987 989 9A9 9AB |
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A98 A9A ABA ABC BA9 BAB BCB BCD CBA CBC CDC CDE DCB DCD DED DEF |
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EDC |
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Base 10 esthetic numbers between 1,000 and 9,999: |
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1010 1012 1210 1212 1232 1234 2101 2121 2123 2321 2323 2343 2345 3210 3212 3232 3234 3432 3434 3454 |
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3456 4321 4323 4343 4345 4543 4545 4565 4567 5432 5434 5454 5456 5654 5656 5676 5678 6543 6545 6565 |
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6567 6765 6767 6787 6789 7654 7656 7676 7678 7876 7878 7898 8765 8767 8787 8789 8987 8989 9876 9878 |
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9898 |
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Base 10 esthetic numbers between 100,000,000 and 130,000,000: |
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101010101 101010121 101010123 101012101 101012121 101012123 101012321 101012323 101012343 |
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101012345 101210101 101210121 101210123 101212101 101212121 101212123 101212321 101212323 |
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101212343 101212345 101232101 101232121 101232123 101232321 101232323 101232343 101232345 |
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101234321 101234323 101234343 101234345 101234543 101234545 101234565 101234567 121010101 |
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121010121 121010123 121012101 121012121 121012123 121012321 121012323 121012343 121012345 |
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121210101 121210121 121210123 121212101 121212121 121212123 121212321 121212323 121212343 |
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121212345 121232101 121232121 121232123 121232321 121232323 121232343 121232345 121234321 |
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121234323 121234343 121234345 121234543 121234545 121234565 121234567 123210101 123210121 |
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123210123 123212101 123212121 123212123 123212321 123212323 123212343 123212345 123232101 |
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123232121 123232123 123232321 123232323 123232343 123232345 123234321 123234323 123234343 |
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123234345 123234543 123234545 123234565 123234567 123432101 123432121 123432123 123432321 |
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123432323 123432343 123432345 123434321 123434323 123434343 123434345 123434543 123434545 |
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123434565 123434567 123454321 123454323 123454343 123454345 123454543 123454545 123454565 |
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123454567 123456543 123456545 123456565 123456567 123456765 123456767 123456787 123456789 |
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</pre> |
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=={{header|Raku}}== |
=={{header|Raku}}== |
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Revision as of 02:25, 18 March 2020
Esthetic numbers is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
An esthetic number is a positive integer where every adjacent digit differs from it neighbour by 1.
- E.G.
- 12 is an esthetic number. One and two differ by 1.
- 5654 is an esthetic number. Each digit is exactly 1 away from its neighbour.
- 890 is not an esthetic number. Nine and zero differ by 9.
These examples are nominally in base 10 but the concept extends easily to numbers in other bases. Traditionally, single digit numbers are included in esthetic numbers; zero may or may not be. For our purposes, for this task, do not include zero (0) as an esthetic number. Do not include numbers with leading zeros.
Esthetic numbers are also sometimes referred to as stepping numbers.
- Task
- Write a routine (function, procedure, whatever) to find esthetic numbers in a given base.
- Use that routine to find esthetic numbers in bases 2 through 16 and display, here on this page, the esthectic numbers from index (base × 4) through index (base × 6), inclusive. (E.G. for base 2: 8th through 12th, for base 6: 24th through 36th, etc.)
- Find and display, here on this page, the base 10 esthetic numbers with a magnitude between 1000 and 9999.
- Stretch: Find and display, here on this page, the base 10 esthetic numbers with a magnitude between 1.0e8 and 1.3e8.
- See also
Phix
<lang Phix>constant aleph = "0123456789ABCDEF" include builtins\ordinal.e
function efill(string s, integer ch, i)
s[i] = ch
for j=i+1 to length(s) do
ch = iff(ch>='1'?iff(ch='A'?'9':ch-1):'1')
s[j] = ch
end for
return s
end function
function esthetic(string s, integer base = 10)
for i=length(s) to 1 by -1 do
integer ch = s[i], cp = iff(i>1?s[i-1]:'Z')
if i>1 and ch<cp and cp<aleph[base] then
ch = iff(ch='8'?'A':iff(ch='9'?'B':ch+2))
return efill(s,ch,i)
elsif i=1 and ch<aleph[base] then
ch = iff(ch='9'?'A':ch+1)
return efill(s,ch,i)
end if
end for
s = "1"&s
return efill(s,'1',1)
end function
string s sequence res for base=2 to 16 do
s = ""
res = {}
for i=1 to base*6 do
s = esthetic(s, base)
if i>=base*4 then
res = append(res,s)
end if
end for
printf(1,"%d%s through %d%s esthetic numbers in base %d\n%s\n",
{base*4,ord(base*4),base*6,ord(base*6),base,join_by(res,1,16)})
end for
s = efill("1000",'1',1) res = {} while length(s)=4 do
res = append(res,s) s = esthetic(s)
end while printf(1,"Base 10 esthetic numbers between 1,000 and 9,999:\n%s\n",
{join_by(res,1,20)})
s = efill("100000000",'1',1) res = {} while s<"130000000" do
res = append(res,s) s = esthetic(s)
end while printf(1,"Base 10 esthetic numbers between 100,000,000 and 130,000,000:\n%s\n",
{join_by(res,1,9)})</lang>
- Output:
8th through 12th esthetic numbers in base 2 10101010 101010101 1010101010 10101010101 101010101010 12th through 18th esthetic numbers in base 3 1210 1212 2101 2121 10101 10121 12101 16th through 24th esthetic numbers in base 4 323 1010 1012 1210 1212 1232 2101 2121 2123 20th through 30th esthetic numbers in base 5 323 343 432 434 1010 1012 1210 1212 1232 1234 2101 24th through 36th esthetic numbers in base 6 343 345 432 434 454 543 545 1010 1012 1210 1212 1232 1234 28th through 42nd esthetic numbers in base 7 345 432 434 454 456 543 545 565 654 656 1010 1012 1210 1212 1232 32nd through 48th esthetic numbers in base 8 432 434 454 456 543 545 565 567 654 656 676 765 767 1010 1012 1210 1212 36th through 54th esthetic numbers in base 9 434 454 456 543 545 565 567 654 656 676 678 765 767 787 876 878 1010 1012 1210 40th through 60th esthetic numbers in base 10 454 456 543 545 565 567 654 656 676 678 765 767 787 789 876 878 898 987 989 1010 1012 44th through 66th esthetic numbers in base 11 456 543 545 565 567 654 656 676 678 765 767 787 789 876 878 898 89A 987 989 9A9 A98 A9A 1010 48th through 72nd esthetic numbers in base 12 543 545 565 567 654 656 676 678 765 767 787 789 876 878 898 89A 987 989 9A9 9AB A98 A9A ABA BA9 BAB 52nd through 78th esthetic numbers in base 13 545 565 567 654 656 676 678 765 767 787 789 876 878 898 89A 987 989 9A9 9AB A98 A9A ABA ABC BA9 BAB BCB CBA 56th through 84th esthetic numbers in base 14 565 567 654 656 676 678 765 767 787 789 876 878 898 89A 987 989 9A9 9AB A98 A9A ABA ABC BA9 BAB BCB BCD CBA CBC CDC 60th through 90th esthetic numbers in base 15 567 654 656 676 678 765 767 787 789 876 878 898 89A 987 989 9A9 9AB A98 A9A ABA ABC BA9 BAB BCB BCD CBA CBC CDC CDE DCB DCD 64th through 96th esthetic numbers in base 16 654 656 676 678 765 767 787 789 876 878 898 89A 987 989 9A9 9AB A98 A9A ABA ABC BA9 BAB BCB BCD CBA CBC CDC CDE DCB DCD DED DEF EDC Base 10 esthetic numbers between 1,000 and 9,999: 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 esthetic numbers between 100,000,000 and 130,000,000: 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
Raku
<lang perl6>use Lingua::EN::Numbers;
sub esthetic($base = 10) {
my @s = ^$base .map: -> \s {
((s - 1).base($base) if s > 0), ((s + 1).base($base) if s < $base - 1)
}
flat [ (1 .. $base - 1)».base($base) ],
{ [ flat .map: { $_ xx * Z~ flat @s[.comb.tail.parse-base($base)] } ] } … *
}
for 2 .. 16 -> $b {
put "\n{(4 × $b).&ordinal-digit} through {(6 × $b).&ordinal-digit} esthetic numbers in base $b";
put esthetic($b)[(4 × $b - 1) .. (6 × $b - 1)]».fmt('%3s').batch(16).join: "\n"
}
my @e10 = esthetic; put "\nBase 10 esthetic numbers between 1,000 and 9,999:"; put @e10.&between(1000, 9999).batch(20).join: "\n";
put "\nBase 10 esthetic numbers between {1e8.Int.&comma} and {1.3e8.Int.&comma}:"; put @e10.&between(1e8.Int, 1.3e8.Int).batch(9).join: "\n";
sub between (@array, Int $lo, Int $hi) {
my $top = @array.first: * > $hi, :k; @array[^$top].grep: * > $lo
}</lang>
- Output:
8th through 12th esthetic numbers in base 2 10101010 101010101 1010101010 10101010101 101010101010 12th through 18th esthetic numbers in base 3 1210 1212 2101 2121 10101 10121 12101 16th through 24th esthetic numbers in base 4 323 1010 1012 1210 1212 1232 2101 2121 2123 20th through 30th esthetic numbers in base 5 323 343 432 434 1010 1012 1210 1212 1232 1234 2101 24th through 36th esthetic numbers in base 6 343 345 432 434 454 543 545 1010 1012 1210 1212 1232 1234 28th through 42nd esthetic numbers in base 7 345 432 434 454 456 543 545 565 654 656 1010 1012 1210 1212 1232 32nd through 48th esthetic numbers in base 8 432 434 454 456 543 545 565 567 654 656 676 765 767 1010 1012 1210 1212 36th through 54th esthetic numbers in base 9 434 454 456 543 545 565 567 654 656 676 678 765 767 787 876 878 1010 1012 1210 40th through 60th esthetic numbers in base 10 454 456 543 545 565 567 654 656 676 678 765 767 787 789 876 878 898 987 989 1010 1012 44th through 66th esthetic numbers in base 11 456 543 545 565 567 654 656 676 678 765 767 787 789 876 878 898 89A 987 989 9A9 A98 A9A 1010 48th through 72nd esthetic numbers in base 12 543 545 565 567 654 656 676 678 765 767 787 789 876 878 898 89A 987 989 9A9 9AB A98 A9A ABA BA9 BAB 52nd through 78th esthetic numbers in base 13 545 565 567 654 656 676 678 765 767 787 789 876 878 898 89A 987 989 9A9 9AB A98 A9A ABA ABC BA9 BAB BCB CBA 56th through 84th esthetic numbers in base 14 565 567 654 656 676 678 765 767 787 789 876 878 898 89A 987 989 9A9 9AB A98 A9A ABA ABC BA9 BAB BCB BCD CBA CBC CDC 60th through 90th esthetic numbers in base 15 567 654 656 676 678 765 767 787 789 876 878 898 89A 987 989 9A9 9AB A98 A9A ABA ABC BA9 BAB BCB BCD CBA CBC CDC CDE DCB DCD 64th through 96th esthetic numbers in base 16 654 656 676 678 765 767 787 789 876 878 898 89A 987 989 9A9 9AB A98 A9A ABA ABC BA9 BAB BCB BCD CBA CBC CDC CDE DCB DCD DED DEF EDC Base 10 esthetic numbers between 1,000 and 9,999: 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 esthetic numbers between 100,000,000 and 130,000,000: 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