Arithmetic Sequences

Question

An arithmetic sequence is a sequence of numbers of the form a,a+n,a+2n,a+3n, etc. In this case, a and n will both be either integers or decimals.

Given two inputs, a, n, and a top number value, return a list of numbers where the last term is less than or equal to the top number value.

The input can be formatted in any way, as well as the output.

The catch to this problem is dealing with floating point arithmetic errors.
For example, 0.1 + 0.3 * 3 is 1, however this will display 0.99999999999... if you simply go 0.1 + 0.3 * 3. We want 1, not 0.99999999999...

Test Cases

a=2, n=3, top=10: [2, 5, 8]
a=3, n=1.5, top=12: [3, 4.5, 6, 7.5, 9, 10.5, 12]
a=3.14159, n=2.71828, top=10: [3.14159, 5.85987, 8.57815]
a=0.1, n=0.3, top=2: [0.1, 0.4, 0.7, 1, 1.3, 1.6, 1.9]

Shortest code wins. Good luck!

Is this supposed to be a standalone program, or a function? If a standalone program is provided, are there any requirements to the format of the input or output? — breadbox, Jun 7, 2012 at 5:11
Function/standalone is fine. There is no specified input or output: the programmer will state both. — beary605, Jun 7, 2012 at 5:49
What do you mean by "floating points" in the first paragraph? If they're actual IEEE754 floating point numbers then most of your test cases don't make sense; so are they strings representing decimal floating point numbers? If so, to what precision? — Peter Taylor, Jun 7, 2012 at 9:33
The input/output part should be specified in the question, not just in the comments. — user unknown, Jun 8, 2012 at 13:41

shiona · Accepted Answer · 2012-06-07 15:04:43Z

6

Non-golfed haskell, 32

f a n t=takeWhile(<=t)[a,a+n..]

I'd love to change takeWhile to take, but integer division can't be done with /, it needs to be done with div. If I go with / then I need to do implicit conversion which makes it that much longer.

answered Jun 7, 2012 at 15:04

shiona

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\$\begingroup\$ That only works without the floating-point problems if called as f :: Rational -> Rational -> Rational -> Rational rather than e.g. Double -> Double -> Double -> Double. But I doubt output in the form [1 % 10,2 % 5,7 % 10,1 % 1,13 % 10,8 % 5,19 % 10] will be accepted. \$\endgroup\$
– ceased to turn counterclockwis
Jun 7, 2012 at 20:17
\$\begingroup\$ @leftaroundabout If it was my problem, I'd accept that output! (But it's not.) \$\endgroup\$
– breadbox
Jun 8, 2012 at 3:32

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marinus · Accepted Answer · 2012-06-07 19:31:34Z

5

APL (22)

{⍵≤T:⍵,∇⍵+N⋄⍬}⊃A N T←⎕

Reads input from stdin as three whitespace-separated numbers.

This is actually shorter than using the index generator.

answered Jun 7, 2012 at 19:31

marinus

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\$\begingroup\$ This problem was actually a fail. Using the print command, or the equivalent of it, rounded off floating points, so the challenge was not a challenge at all. \$\endgroup\$
– beary605
Jun 9, 2012 at 2:44

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Gareth · Accepted Answer · 2012-06-07 11:30:25Z

5

J, 34 33 31 characters

({.+i.@>:@([:<.1{[%~{:-{.)*1{[)

I'm sure there's room for improvement here.

Usage:

   ({.+i.@>:@([:<.1{[%~{:-{.)*1{[)2 3 10
2 5 8

We can give the verb a name for an extra three characters:

   s=.({.+i.@>:@([:<.1{[%~{:-{.)*1{[)
   s 2 3 10
2 5 8

Previously:

((0-.~]*]<:2{[)(((i.100)*1{[)+{.))

Thought I'd have a go at doing this in Golfscript and got as far as .3$- 2$/1+,{2$*}%{3$+}% before realising Golfscript doesn't seem to do floats. Bugger.

edited Jun 7, 2012 at 11:30

answered Jun 7, 2012 at 9:00

Gareth

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Community · Accepted Answer · 2020-06-17 09:04:33Z

4

bash 12:

seq $1 $2 $3

Haha - who would have thought that? Silly'o'bash which normally just handles Integer arithmetic (9/10 = 0) can handle floating points that way:

./cg-6228-arithmetic-sequences.sh 2 3 10
2
5
8
./cg-6228-arithmetic-sequences.sh 3 1.5 12
3,0
4,5
6,0
7,5
9,0
10,5
12,0

Other test-cases omitted for brevity. I have to mention that you can change the locale, if you're irritated by 10,5 which is the continental way to say 10.5. ;)

edited Jun 17, 2020 at 9:04

CommunityBot

1

answered Jun 10, 2012 at 15:49

user unknown

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\$\begingroup\$ How very interesting! \$\endgroup\$
– beary605
Jun 10, 2012 at 16:13
\$\begingroup\$ This could be 3 bytes as a function: seq (maybe) \$\endgroup\$
– CalculatorFeline
Jun 12, 2017 at 17:24

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Cristian Lupascu · Accepted Answer · 2012-06-07 19:10:16Z

3

Ruby 34

s=->a,n,t{p a;s[a+n,n,t]if a+n<=t}

Input: the three function parameters

Output: the sequence numbers are printed, one per line

Ideone link: http://ideone.com/SahPs

edited Jun 7, 2012 at 19:10

answered Jun 7, 2012 at 8:42

Cristian Lupascu

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ephemient · Accepted Answer · 2012-06-08 05:40:00Z

3

J, 26

s=:1 :']+u*[:i.@<.@>:u%~-'

There's some interesting syntax to use this definition.

   10(2 s)1
1 3 5 7 9

answered Jun 8, 2012 at 5:40

ephemient

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Jon · Accepted Answer · 2012-06-14 19:23:46Z

3

Ruby - 28

((t-a)/n).times{|i|p(a+i*n)}

answered Jun 14, 2012 at 19:23

Jon

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Community · Accepted Answer · 2020-06-17 09:04:33Z

3

Mathematica, 5 bytes

Range

Arguments are a,top,n in that order. I'm assuming that decimal points at the end are okay.

edited Jun 17, 2020 at 9:04

CommunityBot

1

answered Mar 5, 2016 at 1:34

CalculatorFeline

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Community · Accepted Answer · 2020-06-17 09:04:33Z

2

Scala 52

val x,?,z=BigDecimal(readLine)
x to z by?map println

Give inputs a,n and top in the separate line. Each entry of the output will be listed in the separate line.

edited Jun 17, 2020 at 9:04

CommunityBot

1

answered Jun 7, 2012 at 5:40

Prince John Wesley

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Community · Accepted Answer · 2020-06-17 09:04:33Z

2

Mathematica 39 37

Table[#+#2 k,{k,0,Quotient[#3-#,#2]}]&

Usage

Table[#1 + #2 k, {k, 0, Quotient[#3 - #1, #2]}] &[2, 3, 10]
Table[#1 + #2 k, {k, 0, Quotient[#3 - #1, #2]}] &[3, 1.5, 12]
Table[#1 + #2 k, {k, 0, Quotient[#3 - #1, #2]}] &[3.14159, 2.71828, 10]
Table[#1 + #2 k, {k, 0, Quotient[#3 - #1, #2]}] &[0.1, 0.3, 2]

sequence output

edited Jun 17, 2020 at 9:04

CommunityBot

1

answered Aug 25, 2012 at 21:05

DavidC

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Bbrk24 · Accepted Answer · 2021-08-30 04:49:46Z

Swift, 90

Not quite as short as the other ones here but this doesn't use a builtin to compute the sequence, nor does it operate on a standard float type. It declares a function f(a:n:t:) that takes the numbers in and prints the sequence to stdout.

import Foundation
func f(a:Decimal,n:Decimal,t:Decimal){var x=a
while x<=t{print(x)
x+=n}}

Try it Online! (with hardcoded test case)

I learned a few things while doing this that surprised me:

Swift's range builtin is only iterable for integers, unlike in Python where you can specify the step size.
Assignment operators in Swift return Void, so I couldn't abbreviate the body of the while loop to print(x+=n). I tried it; it just printed () a bunch of times.
Decimal values are not converted to Double when printing. If you replace Decimal in the declaration with Double, it prints 1.0 and 1.9000000000000001 rather than 1 and 1.9. On the other hand, this proves that it is avoiding floating-point rounding errors, as the question specified.
There is no version of the <= operator that lets you compare a Decimal to any other number type, so I can't make the function declaration shorter by changing t's type.
- In fact, even though Decimal is ExpressibleByFloatLiteral, it is not FloatingPoint.

You could shave off two bytes by allowing the input to be mutated (changing the function signature to f(a:inout Decimal,n:Decimal,t:Decimal), as this eliminates the need for the variable x.

Griffin · Accepted Answer · 2012-06-07 01:55:15Z

1

JavaScript 70

s=prompt().split(",");for(n=0;(p=s[0]-0+n*s[1]-0)<=s[2]-0;n++)alert(p)

input in the form a,n,top

answered Jun 7, 2012 at 1:55

Griffin

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\$\begingroup\$ The code gives floating-point arithmetic errors. I, however, used a different test case: I will add it to the list. \$\endgroup\$
– beary605
Jun 7, 2012 at 5:08

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breadbox · Accepted Answer · 2012-06-07 05:53:55Z

1

Perl, 37 chars

for(($_,$n,$t)=<>;$_<=$t;$_+=$n){say}

Input a, n, and top, each number on a separate line. The list is output with newlines separating the values. Run with perl -M5.010 (or perl -E).

answered Jun 7, 2012 at 5:53

breadbox

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beary605 · Accepted Answer · 2012-06-07 06:15:01Z

Python (245)

Input should be given with a space in between, e.x. 0.1 0.3 0.5

a=raw_input().split()
I,F=int,float
D='.'
b=[[I(i.replace(D,'')),len(i.split(D)[1:])]for i in a[:2]]
a=map(F,a)
c=max(b,key=lambda x:x[1])[1]
for i in b:i[0]*=10**(c-i[1])
print [(b[0][0]+i*b[1][0])/10.0**c for i in range(I((a[2]-a[0])/a[1]+1))]

It avoids floating point errors by turning each floating point into a list containing two values: the number without the decimal point, and the number of significant digits. example: 1.34 -> [134, 2]

grc · Accepted Answer · 2012-06-07 06:41:10Z

0

Python, 37

a,n,t=input()
while a<=t:print a;a+=n

Grabs input in the form a, n, top, and prints out the numbers on separate lines.

answered Jun 7, 2012 at 6:41

grc

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Cristian Lupascu · Accepted Answer · 2012-06-07 11:59:05Z

0

C# 120 74

void A(float a,float n,int t){Console.Write(a+" ");a+=n;if(a<=t)A(a,n,t);}

Edit: New version - recursive and a lot shorter than using LINQ :)

Input: the three parameters of method A

Output: the numbers in the sequence are printed to console, separated by spaces.

Test link: http://ideone.com/o7g6k

Previous version (using LINQ):

IEnumerable<float>A(float a,float n,int t){return Enumerable.Range(0,int.MaxValue).Select(i=>a+n*i).TakeWhile(s=>s<=t);}

edited Jun 7, 2012 at 11:59

answered Jun 7, 2012 at 8:27

Cristian Lupascu

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TwoScoopsofPig · Accepted Answer · 2012-06-07 20:44:48Z

0

PHP 83

<?function a($x,$i,$t){while($r<$t){$r=$x+$i*$g++;$s.=($r<$t?$r." ":"");}echo$s;}?>

Wish I could remove "function" but there's no shorter declaration for that in PHP. Handy that PHP uses untyped variables!

Usage: a(2,3,10); Returns: 2 5 8

edited Jun 7, 2012 at 20:44

answered Jun 7, 2012 at 18:35

TwoScoopsofPig

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1

\$\begingroup\$ You can save two bytes by omitting the final ?>. \$\endgroup\$
– breadbox
Jun 8, 2012 at 3:36

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Community · Accepted Answer · 2020-06-17 09:04:33Z

0

PHP, 53

<?for(list(,$a,$n,$x)=$argv;$a<=$x;$a+=$n)echo"$a ";

edited Jun 17, 2020 at 9:04

CommunityBot

1

answered Jun 8, 2012 at 2:29

l0n3sh4rk

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mnel · Accepted Answer · 2016-03-05 11:34:17Z

0

R, 3 bytes

seq

Built in function with arguments from (a), to (top) and by (n)

usage seq(a,top,n) eg

seq(2,10,3)

output numeric vector

2 5 8

answered Mar 5, 2016 at 11:34

mnel

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Community · Accepted Answer · 2020-06-17 09:04:33Z

0

TI-Basic, 20

Prompt A,N,T:For(I,A,T,N:Disp I:End

edited Jun 17, 2020 at 9:04

CommunityBot

1

answered Apr 5, 2016 at 23:32

Timtech

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Razetime · Accepted Answer · 2020-10-13 09:33:22Z

0

Husk, 7 bytes

↑≤⁰¡+⁴²

Try it online!

answered Oct 13, 2020 at 9:33

Razetime

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Stack Exchange Network

Arithmetic Sequences

Test Cases

21 Answers 21

Non-golfed haskell, 32

APL (22)

J, 34 33 31 characters

bash 12:

Ruby 34

J, 26

Ruby - 28

Mathematica, 5 bytes

Scala 52

Mathematica 39 37

Swift, 90

JavaScript 70

Perl, 37 chars

Python (245)

Python, 37

C# 120 74

PHP 83

PHP, 53

R, 3 bytes

TI-Basic, 20

Husk, 7 bytes

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Arithmetic Sequences

Test Cases

21 Answers 21

Non-golfed haskell, 32

APL (22)

J, 34 33 31 characters

bash 12:

Ruby 34

J, 26

Ruby - 28

Mathematica, 5 bytes

Scala 52

Mathematica 39 37

Swift, 90

JavaScript 70

Perl, 37 chars

Python (245)

Python, 37

C# 120 74

PHP 83

PHP, 53

R, 3 bytes

TI-Basic, 20

Husk, 7 bytes

Your Answer

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