Digit Sum Integer Sequence (working title)
Inspired by this challenge. If anyone has any suggestions for a song title I could use for the challenge title then please leave a comment.
Definition
We define f(x)
for a given integer as the sum of:

x
itself, 
s
, the smallest digit in the decimal representation ofx
, and, 
l
, the largest digit in the decimal representation ofx
Examples
x 
s 
m 
f(x) 

2  2  2  6 
53  3  5  61 
77  7  7  91 
123  1  3  127 
8022  0  8  8030 
Challenge
You will be building a sequence by repeatedly applying f(x)
to a starting value n>0
taken as input, with the first term in the sequence being n
itself.
For example, given a starting value of n=1
, the first few terms go as follows:
1, 3, 9, 27, 36, 45, 54, 63, ...
You will also take an integer i
as input and then either:
 Output the
i
^{th} term (0indexed or 1indexed, but please specify) of then
based sequence,  Output the the first
i
terms of that sequence, or,  Forego taking
i
as input and output then
based sequence infinitely.
Rules
 I/O can be by any reasonable, convenient means.
 This is codegolf so lowest byte count in each language wins.
Test Cases
Here are the first 25 terms of each sequence from n=1
to n=10
:
1, 3, 9, 27, 36, 45, 54, 63, 72, 81, 90, 99, 117, 125, 131, 135, 141, 146, 153, 159, 169, 179, 189, 199, 209
2, 6, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 117, 125, 131, 135, 141, 146, 153, 159, 169, 179, 189, 199, 209
3, 9, 27, 36, 45, 54, 63, 72, 81, 90, 99, 117, 125, 131, 135, 141, 146, 153, 159, 169, 179, 189, 199, 209, 218
4, 12, 15, 21, 24, 30, 33, 39, 51, 57, 69, 84, 96, 111, 113, 117, 125, 131, 135, 141, 146, 153, 159, 169, 179
5, 15, 21, 24, 30, 33, 39, 51, 57, 69, 84, 96, 111, 113, 117, 125, 131, 135, 141, 146, 153, 159, 169, 179, 189
6, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 117, 125, 131, 135, 141, 146, 153, 159, 169, 179, 189, 199, 209, 218
7, 21, 24, 30, 33, 39, 51, 57, 69, 84, 96, 111, 113, 117, 125, 131, 135, 141, 146, 153, 159, 169, 179, 189, 199
8, 24, 30, 33, 39, 51, 57, 69, 84, 96, 111, 113, 117, 125, 131, 135, 141, 146, 153, 159, 169, 179, 189, 199, 209
9, 27, 36, 45, 54, 63, 72, 81, 90, 99, 117, 125, 131, 135, 141, 146, 153, 159, 169, 179, 189, 199, 209, 218, 227
10, 11, 13, 17, 25, 32, 37, 47, 58, 71, 79, 95, 109, 118, 127, 135, 141, 146, 153, 159, 169, 179, 189, 199, 209
More test cases can be generated using this ungolfed Japt implementation, where the first integer in the header is n
and the second is i
.
[jq], 38 bytes while(1; …
4mo ago
[Haskell], 56 bytes …
4mo ago
Ruby, 36 bytes Infinite ver …
5d ago
[Python 3], 183 181 175 bytes …
4mo ago
4 answers
jq, 38 bytes
while(1;.+("\(.)"explodemax+min96))
prints the infinite sequence starting with $n$.
0 comment threads
Ruby, 36 bytes
Infinite version:
n=1;0while n+=p(n).digits.minmax.sum
Try this online!
(program is interrupted after it reaches the 128KiB limit of output)
0 comment threads
Python 3, 183 181 175 bytes
def f(a,b):
c=a;a=str(a)
for i in range(b):
y=0;z=9
for j in range(len(a)):
if y<int(a[j]):y=int(a[j])
if z>int(a[j]):z=int(a[j])
c=int(a)+y+z;a=str(c)
print(c)
I decided to go for outputting the i
th value of the sequence, 0indexed. a
is the number to be sequenced and b
is the index of the nonexistent listsince no list existsto be printed.
1 comment thread