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Challenges

Digit Sum Integer Sequence (working title)

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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 of x, and,
  • l, the largest digit in the decimal representation of x

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 the n-based sequence,
  • Output the the first i terms of that sequence, or,
  • Forego taking i as input and output the n-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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Regarding title (1 comment)

3 answers

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Haskell, 56 bytes

f a=a:f(a+g(read.pure<$>show a))
g a=minimum a+maximum a

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jq, 38 bytes

while(1;.+("\(.)"|explode|max+min-96))

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prints the infinite sequence starting with $n$.

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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)

Try it online!

I decided to go for outputting the ith value of the sequence, 0-indexed. a is the number to be sequenced and b is the index of the non-existent list--since no list exists--to be printed.

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