Find $2000$ th term of below sequence
$$2,3,5,6,7,8,10,\ldots$$

(the sequence contains positive integers other than perfect squares)

Question

Find $2000$ th term of below sequence 
$$2,3,5,6,7,8,10,\ldots$$

(the sequence contains positive integers other than perfect squares)

nnesha · Answer

$\huge\color{white}{{ *}}$

nincompoop · Answer

993

nincompoop · Answer

my bad

nincompoop · Answer

1993

nincompoop · Answer

sequence of a number that are not squares

ganeshie8 · Answer

thats very close ! but it has to be greater than 2000 for sure... as the 2000th term of positive integer sequence(1,2,3,4,...) itself is 2000. i am looking for answer and a neat way to justify the answer :)

nincompoop · Answer

the 2000th term is 2000? I do not think so.  We started with 2 and skipped 4 and 9 
that is down to 10 - 3 sequence

ganeshie8 · Answer

2000th term of below sequence is 2000 :
$$1,2,3,4,5, \ldots$$

so the 2000th term of the sequence in main question has to be greater than 2000

nincompoop · Answer

ohh hahahha

nincompoop · Answer

right

nincompoop · Answer

can I just give you the pseudo-code in Python or C++? laughing out loud

ganeshie8 · Answer

lol it can be considered a sledgehammer in the context of this problem :P

anonymous · Answer

2044?

anonymous · Answer

till 2000.. 44 squares are missing from the series last of which is 1936.. so 2044

ganeshie8 · Answer

thats very close too.. but no!

anonymous · Answer

then 2045?

ganeshie8 · Answer

2045 is right ! :)

nincompoop · Answer

how do I interpret this? 
$a_n = \lfloor \sqrt{n}+\frac{1}{2})\rfloor +n$

ganeshie8 · Answer

that looks interesting xD
is that the general term of sequence ?

nincompoop · Answer

it is, apparently

nincompoop · Answer

don't mind me, I am crashing from the caffeine-induced waking state

ganeshie8 · Answer

that actually works! http://www.wolframalpha.com/input/?i=floor%28sqrt%282000%29%2B1%2F2%29%2B2000

anonymous · Answer

2045?
1935:1979
1956:2000
1980:2024
1981:2026
2000:2045

ikram002p · Answer

i thought of it like this sequence of perfect square up to some value http://www.wolframalpha.com/input/?i=n%5E2+from+n%3D1+to+n%3D50 so we can note that 2000-44=1956 so the 1956 term is 2000 now we keep moving like this 2001.. to 2024 ( the 1980 term ) now we need other 20 terms :P from 2026 .... to 2045 so i would say 2045

mathslover · Answer

Suscribing to the post :P

mathslover · Answer

Oops *Subscribing

jaynator495 · Answer

oh hia der...

kainui · Answer

Yeah I like @ikram002p 's way, that's how I was gonna do it haha.