In the cyclic number 142857 the digits at right gradually shift to the left on multiplication by 5,4,6,2 and 3.viz producing 714285,571428,857142,285714 and 428571.This cyclic number is actually found by taking the reciprocal of the prime number 7.viz in the reciprocal the group of digits 1,4,2,8,5,7 repeat continuously..
You can find more cyclic numbers by finding similarly the reciprocals of more prime numbers or multiples of prime numbers.
If you take the reciprocals of numbers having 2 digits or more you will face with one or more zeros at the beginning,like 076923 for 13.......,012345679 for 81.....00729927 for 137 etc and you should allow the zeros to remain while making the multiplications.
Now I am presenting a cyclic number with six zeros in the beginning.
The same is 00000048269001213 and this can be found by taking the reciprocal of the prime 2071723.
If you multiply this with the number 621517,you will find the last digit at right viz 3 moving to the front viz producing 30000004826900121.You can see that except for 3 all the other digits appear in the product in the same order.
I shall inform you later how this number 621517 used for multiplication has been found.I am in the process of finding more numbers which when used for multiplication allow the other digits at right to gradually move to the left.There is a method for finding them but because the numbers are large,the process is not easy and will take time.
You can find more cyclic numbers by finding similarly the reciprocals of more prime numbers or multiples of prime numbers.
If you take the reciprocals of numbers having 2 digits or more you will face with one or more zeros at the beginning,like 076923 for 13.......,012345679 for 81.....00729927 for 137 etc and you should allow the zeros to remain while making the multiplications.
Now I am presenting a cyclic number with six zeros in the beginning.
The same is 00000048269001213 and this can be found by taking the reciprocal of the prime 2071723.
If you multiply this with the number 621517,you will find the last digit at right viz 3 moving to the front viz producing 30000004826900121.You can see that except for 3 all the other digits appear in the product in the same order.
I shall inform you later how this number 621517 used for multiplication has been found.I am in the process of finding more numbers which when used for multiplication allow the other digits at right to gradually move to the left.There is a method for finding them but because the numbers are large,the process is not easy and will take time.
No comments:
Post a Comment