Pattern Recognition - 91

Find out the next two numbers in the series.

512132 , 23121, 1213 , 312, _ , _ ,..............

Answer

Tn=   Reverse form (Remove first digit of Tn-1)

512132 ---> Reverse(12132 ) -----> 23121
23121  ----> Reverse(3121)   ------>1213
1213    ----->Reverse (213)    ------>312

Next two numbers  
312   ----->Reverse (12)    ------>21
21   ----->Reverse (1)    ------>1

512132 , 23121, 1213 , 312, 21 , 1,..............

Pattern Recognition- 90

Find out the next two numbers in the series.

49, 2549 , 121169 , 289361, _ ,_ ,.......


Answer

49    -->  4 , 9
2549 -->  25,49
121169 --> 121 , 169
289361--->289 , 361

4 ,9 , 25 ,49 , 121, 169 , 289, 361 , ................

4= 2 * 2
9=3 * 3
25 =5 * 5
49=7 * 7
121 =11 * 11
169 =13 * 13
289= 17 * 17
361 =19 * 19
  
Tn=n * n  where n  is a  prime number
 
Next four prime numbers 23 , 29, 31 ,37

Next two numbers (23 *23 ) (29 *29) -- >529841
                          (31 * 31) (37 * 37)--> 9611369

49, 2549 , 121169 , 289361,  529841, 9611369,................

Pattern Recognition - 89

Find out the next two numbers in the series.

1,1 ,2 ,4 , 7 , 13 , 24 , 44 , _ , _ ,.......


Answer

Have you heard about Fibonacci series?
Fibonacci number - Wikipedia, the free encyclopedia
Tn= Tn-1 + Tn-2

Given series is not Fibonacci but similar to that

Tn=Tn-1 + Tn-2 +Tn-3

4   = 1+ 1 +2
7   = 4 + 2 +1
13 = 2 + 4 +7
24 =4  +7  +13
44 =7 +13 +24

Next two numbers    13+24+44 = 81
                                24+44+81 =149

1,1 ,2 ,4 , 7 , 13 , 24 , 44 , 81 , 149 ,.......

Pattern Recognition -88

Find out the next two numbers in the series.

23 , 35 , 58 , 812 , 1217 , 1723 , _ , _ , ......................


Answer

23 , 35 , 58 , 812 , 1217 , 1723 , _ , _ , ......................

23 , 35 , 58 , 812 , 1217 , 1723 , _ , _ , ......................

23 , 35 , 58 , 812 , 1217 , 1723 , _ , _ , ......................

23 , 35 , 58 , 812 , 1217 , 1723 , _ , _ , ......................

23 , 35 , 58 , 812 , 1217 , 1723 , _ , _ , ......................

2   3 , 3      5 , 5      8 , 8    12 , 12       17 , 17      23 , _ , _ , ......................
  +1      +2         +3        +4         +5              +6 

Next two numbers    23  23+7  = 2330  
                              30  30+8  = 3038

23 , 35 , 58 , 812 , 1217 , 1723 , 2330 , 3038 , ......................

Pattern Recognition - 87

Find out the next two numbers in the series.

2529, 3531, 4548 , 5552 , _ , _ , ........................


Answer

2529, 3531, 4548 , 5552 , _ , _ , ........................

29 = 25+4 

31 = 35- 4  

48 = 45 +3

52 = 55 - 3 


Next two numbers   65 65+2    75  75-2     6567    7573


2529, 3531, 4548 , 5552 , 6567 , 7573 , ........................ 

Pattern Recognition -86

Find out the next two numbers in the series.

585431 , 135431 , 45431 ,9431, 1331,_ , _, .............. 


Answer

585431 , 135431 , 45431 ,9431, 1331,_ , _, ..............   5+8 =13

585431 , 135431 , 45431 ,9431, 1331,_ , _, ..............   1+3 =4

585431 , 135431 , 45431 ,9431, 1331,_ , _, ..............   4+5 =9

585431 , 135431 , 45431 ,9431, 1331,_ , _, ..............  9+4 =13

Next two numbers

1+3 =4               ------> 431

431 ---- 4+3 =7   ----->71

585431 , 135431 , 45431 ,9431, 1331,431 , 71, ..............

Pattern Recognition-85

Find out the next two numbers in the series.

100, 101100, 110111100, 1000101011100,_, _,......

Answer

If we convert the above numbers to decimal

100,  101100,  110111100,  1000101011100 ,_ , _ ,......

4     , 44        ,     444        ,    4444               ,_ , _ ,..............

Next two numbers    44444, 444444

44444 -----> 1010110110011100

444444 ----> 1101100100000011100

100, 101100, 110111100, 1000101011100, 1010110110011100  , 1101100100000011100 ,......