If you try to count using only numbers with all its digits in ascending order, you will get this:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 44, 45, 46, 47, 48, 49, 55, 56, 57, 58, 59, 66, 67, 68, 69, 77, 78, 79, 88, 89, 99, 111, 112, 113, 114, 115, 116, 117, 118, 119, 122, 123, ...
This sequence is registered in OEIS as A009994 - Numbers with digits in nondecreasing order.
Note that all the jumps are located after the last digit becomes 9, because the digit 0 cannot appear after the first occurrence. Considering this, I have created a little Perl program to generate it:
#!/usr/bin/perl
for($_="";;) {
s/([0-8]?)(9*)$/$2?($1?$1+1:1)x(length($2)+1):length($1)?$1+1:0/e;
print "$_\n";
}
On each iteration, the regular expression is applied to the variable $_ generating the next number, following this algorithm:
- If there are one or more 9's at the end then:
- If there is a digit X<9 just before the 9's then that digit X and those 9's are all replaced with the digit X+1 repeated as many times as the number of 9's plus one, for example 22499=>22555
- If there is no digit just before the 9's then is considered that the digit is 0 and the same operation is done, for example 999=>1111
- If there are no 9's at the end then:
- If there is a digit X at the end then the digit X is replaced with the digit X+1, for example 133=>134
- If there is no digit in the number then the digit 0 is inserted
I tried to do the code as easy to understand as I could, so you can use it if you need without problem ;-). Thanks for reading!
