ASSIST  Assistance Required
After the 1997/1998 Southwestern European Regional Contest (which was held in Ulm) a large contest party took place. The organization team invented a special mode of choosing those participants that were to assist with washing the dirty dishes. The contestants would line up in a queue, one behind the other. Each contestant got a number starting with 2 for the first one, 3 for the second one, 4 for the third one, and so on, consecutively.
The first contestant in the queue was asked for his number (which was 2). He was freed from the washing up and could party on, but every second contestant behind him had to go to the kitchen (those with numbers 4, 6, 8, etc). Then the next contestant in the remaining queue had to tell his number. He answered 3 and was freed from assisting, but every third contestant behind him was to help (those with numbers 9, 15, 21, etc). The next in the remaining queue had number 5 and was free, but every fifth contestant behind him was selected (those with numbers 19, 35, 49, etc). The next had number 7 and was free, but every seventh behind him had to assist, and so on.
Let us call the number of a contestant who does not need to assist with washing up a lucky number. Continuing the selection scheme, the lucky numbers are the ordered sequence 2, 3, 5, 7, 11, 13, 17, etc. Find out the lucky numbers to be prepared for the next contest party.
Input Specification
The input contains several test cases.
Each test case consists of an integer n
.
You may assume that 1 <= n <= 3000
.
A zero follows the input for the last test case.
Output Specification
For each test case specified by n
output on a single line the n
th lucky number.
Sample Input
1 2 10 20 0
Sample Output
2 3 29 83
hide comments
code_inception:
20161112 11:50:43
@praney_rai read the question creafully ..... after 5 every fifth person goes for assistance i.e., 19 35 49 not 10 15 20 25 .....


praney_rai:
20160930 09:23:40
20 th prime number is 71 but here it is shown 83. is there any misunderstanding


praval_singhal:
20160618 18:27:35
I tried a lot but couldn't perform better than 0.02s. Any Suggestions by those who got 0.00s. Thanks in Advance. 

sravanthreddy:
20160324 19:25:32
use sieve==>bruteforce... ;) AC yay!


gullu_mishra:
20160312 08:18:34
dont think too much ...use brute force ... ;) 

dwij28:
20160102 11:28:41
AC using a sieve. I tried for 5 minutes but could not think of an O(1) solution or a formula. Is O(1) possible ? 

:.Mohib.::
20150610 09:31:52
Easy ;) 
Added by:  Wanderley GuimarÄƒes 
Date:  20070921 
Time limit:  0.566s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JS 
Resource:  University of Ulm Local Contest 2003 