What is the mathematical sequence 1,2,2,3,3,3,4,4,4,4....?

Question

Essentially it's one 1, two 2's, three 3's, four 4's, five 5's, six 6's, seven 7's and so on.

Thanks!

Answer 1

If you're looking for a formula, then the nth term of this sequence is

[√(2n + 0.25)] - 0.5, ignoring anything after the decimal point.

---

If this isn't what you're looking for, then I'm not sure what you mean by "what is." It is what it is. The sequence of numbers you've described. It doesn't have a special name as far as I know.

---

EDIT: This sequence is the inverse integer sequence of the triangular numbers. (The triangular numbers are 1, 1 + 2, 1 + 2 + 3, 1 + 2 + 3 + 4, and so on.)

The nth term in this sequence tells you the index of the first element in the sequence of triangular numbers which is greater than or equal to n.

I found my formula by computing the inverse function of the formula for the nth triangular number: y = (1/2)(x^2 + x).

Answer 2

thats the mathmatical sequence

Answer 3

There are other functions for the nth term too.

Here is the page in the online encyclopedia of integer sequences:

http://www.research.att.com/~njas/sequen...

.