Lucky Number

Number Theory Level 5

Each number of a sequence of positive integers is obtained from the previous term by adding the largest digit. These numbers are called Lucky Number \color{#20A900}{\text{ Lucky Number } } . What is the maximum number of successive odd terms in such a sequence?


The answer is 5.

Anish Harsha by Anish Harsha , 20, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Lu Chee Ket
Nov 30, 2015

Here is the Lucky Number being interpreted: 

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
 
1       0   0   0   0   1       1   1   1   1       1           
2       0   0   0   0   2       2   2   2   2                   
4       0   0   0   0   4       4   4   4   4                   
8       0   0   0   0   8       8   8   8   8                   
16      0   0   0   1   6       6   6   6   6                   
22      0   0   0   2   2       2   2   2   2                   
24      0   0   0   2   4       4   4   4   4                   
28      0   0   0   2   8       8   8   8   8                   
36      0   0   0   3   6       6   6   6   6                   
42      0   0   0   4   2       4   4   4   4                   
46      0   0   0   4   6       6   6   6   6                   
52      0   0   0   5   2       5   5   5   5                   
57      0   0   0   5   7       7   7   7   7       1           
64      0   0   0   6   4       6   6   6   6                   
70      0   0   0   7   0       7   7   7   7                   
77      0   0   0   7   7       7   7   7   7       1           
84      0   0   0   8   4       8   8   8   8                   
92      0   0   0   9   2       9   9   9   9                   

...

87807       8   7   8   0   7       7   8   8   8       1
87815       8   7   8   1   5       5   8   8   8       1
87823       8   7   8   2   3       3   8   8   8       1
87831       8   7   8   3   1       3   8   8   8       1
87839       8   7   8   3   9       9   9   9   9       1
87848       8   7   8   4   8       8   8   8   8       
87856       8   7   8   5   6       6   8   8   8       
87864       8   7   8   6   4       6   8   8   8       
87872       8   7   8   7   2       7   8   8   8

3 consecutive terms are more frequent to occur occasionally when we observe by Excel simulation. Observed that a 9 stop the sequence. Maximum of 5 up to 5 digits. Can be confirmed with further investigation.

Answer: 5 \boxed{5}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Wrong. This solution made no sense.

Pi Han Goh - 5 years, 5 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...