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!

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 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. ;)

Answer 5

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

Answer 6

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

Answer 7

Ruby - 28

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

Answer 8

Mathematica, 5 bytes

Range

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

Answer 9

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.

Answer 10

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]

Answer 11

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

Answer 12

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).

Answer 13

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]

Answer 14

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.

Answer 15

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);}

Answer 16

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

Answer 17

PHP, 53

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

Answer 18

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  

Answer 19

TI-Basic, 20

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