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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:
-
xitself, -
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
ith term (0-indexed or 1-indexed, but please specify) of then-based sequence, - Output the the first
iterms of that sequence, or, - Forego taking
ias input and output then-based sequence infinitely.
Rules
- I/O can be by any reasonable, convenient means.
- This is code-golf 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.
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Post
Dyalog APL, 23 bytes
{⍵+(⌈/+⌊/)10⊥⍣¯1⊢⍵}⍣⎕⊢1⎕
Takes an input n and outputs the 0-indexed nth item of the sequence.
{⍵+(⌈/+⌊/)10⊥⍣¯1⊢⍵}⍣⎕⊢⎕
⊢⎕ ⍝ Starting from <input>,
⍣⎕ ⍝ repeat <input> times
⍵+ ⍝ the number plus
(⌈/+⌊/) ⍝ the minimum plus the maximum of
10⊥⍣¯1 ⍝ the base-10 representation
⊢⍵ ⍝ of the number.
💎
Created with the help of Luminespire.
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