Generating a sequence of lists

Question

I have learnt how to generate a sequence of numbers, but now I come across a question whether it is possible to generate e sequence of lists. Say, I would like to generate {1},{1,2},{1,2,3},...,{1,2,3,...,10}. How can I do that?

@JasonB: What? Hahaha... That really works. I am new in Mathematica. And haven't learnt that symbol '@'. Could you explain? — Chen M Ling, Apr 15 '16 at 10:44
So Range[x] will give {1, 2, 3, 4, 5,......x}, and /@ is the infix notation for Map. As an example, look f /@ {1, 2, 3} gives {f[1], f[2], f[3]}. So in the above, Range[10] gives {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, and then I'm just mapping Range onto that list — Jason B., Apr 15 '16 at 10:47
at least closely related: generate successive sublists from a list? — Kuba, Apr 15 '16 at 11:46

score 4 · Accepted Answer · answered Apr 15 '16 at 11:40

4

Try this:

Table[Range[i], {i, 1, 10}]

(*  {{1}, {1, 2}, {1, 2, 3}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}, {1, 2, 3, 4, 
  5, 6}, {1, 2, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 6, 7, 8}, {1, 2, 3, 4,
   5, 6, 7, 8, 9}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}} *)

or this:

Table[Table[k, {k, 1, i}], {i, 1, 10}]

with the same result. Have fun!

answered Apr 15 '16 at 11:40

Alexei Boulbitch

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Yes. That generates the same result. Thanks :) – Chen M Ling Apr 15 '16 at 11:45

score 2 · Answer 2 · answered Apr 15 '16 at 16:04

2

My entry into the obfuscated Mathematica competition for April, 2016.

rangeList[n_Integer?Positive] := NestList[Join[#, {Last[#] + 1}] &, {1}, n - 1]

rangeList[5]

{{1}, {1, 2}, {1, 2, 3}, {1, 2, 3, 4}, {1, 2, 3, 4, 5}}

Too bad I'm posting this on April 15 rather than April 1.

answered Apr 15 '16 at 16:04

m_goldberg

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FoldList[(Flatten@*List), Nothing, Range[10]] == Range@Range[10] – user1066 Apr 15 '16 at 17:29

Generating a sequence of lists

2 Answers2