Friday, 26 October 2012

Kaprekar constant 5 digits-rejoinder

With reference to my earlier post date 10 sep 2012,I have to indicate the following details-
There is no constant of 5 digits like 74943 and 82962 as mentioned by me.
However there appear 2 series in which these 2 numbers are included.
For instance,we can start with the digits 2,3,5,8 and 9
The difference between the highest number 98532 and the smallest number 23589 formed with these digits is
of course 74943.Using these new set of digits viz 3,4,4,7 and 9 we do not get back 74943 ,in which case only we can treat 74943 as a Kaprekar constant like 6174 you get with 4 digit numbers.
In fact you get 97443-34479=62964.
You repeat now and get 96642-24669=71973
Again repeat you get 97731-13779=83952.
Repeat again,only now you get back 74943.as the same digits 2,3,5,8 and 9 are now involved.
Thus 74943 forms part of the series 74943,62964,71973,83952,74943...repeated back.
Similarly the other number 82962 forms part of the series 82962,75953,63954,61974,82962 repeated back.
You can in fact say if you like that all the 8 numbers involved are Kaprekar constants,instead of only one number like 6174 involved with 4 digits. 

Sunday, 7 October 2012

Sequences-4 EMIRPS sequence

The next sequence in my list is the EMIRP sequence of numbers
If you guess correctly these are PRIME numbers which remain prime even when you read from right to left
Some examples are 13,31,17,71,37,73,79,97,101,113,149,157 etc.
The sequence has the number A 006567 in the OEIS website.

Sequences-3 Look and say sequence.

My next sequence is Look and say"" number sequence.The sequence can start with any number say 1.You look at it and say one 1. The next number is thus 11.You look at this and say two one.The next number is thus 21.You look at this and say one two one one.The next number is thus 1211.You proceed accordingly and make more numbers.The list will thus be 1,11,21,1211,111221,312211,13112221,1113213211 ..etc
This comes under the OEIS website number A 005150..

Saturday, 6 October 2012

Sequences-2 RATS sequence

Let me now tell you about another sequence.
This also has a peculiar name called  RATS sequence of numbers.
I believe it is based on the procedure of  starting  with a number Reversing it,Adding it to make a Total and Sorting it.
For example if 668 is a number in the sequence,the procedure gives us 668+866=1534,which when sorted to give a number in ascending order gives us 1345,which is the next number in the sequence.Next to this comes from 1345+5431=6776,which when sorted gives us 6677.Similarly the next can be found to be 13444.
The full list of numbers in the sequence is 1,2,4,8,16,77,145,668,1345,6677,13444,55778,  133345
666677,1333444,5567777,1233345,66666677,133333444 and so on.You can see repetition of digits like 3, 6 etc
In the website OEIS referring to the online encyclopedia of integer sequences,this sequence has the number  A004000

Friday, 5 October 2012

Sequences-1 EBAN number sequence

Let me introduce some sequences
The one I first wish to introduce has a funny name.
It is called eban number sequence.
When you write down the names of the numbers in English in this sequence the alphabet E
will be found  banned
The numbers are 2,4,6,30,32,34,36,40,42,44,50,52,54,56,60,62,64,66 and so on.