In an earlier blog under my account Nadamadum numbers,I had dealt with generator 41 and the corresponding cyclic number of 5 digits viz 02439.
I am now presenting details about another 5 digit cyclic number 00369 from 271 operating as the generator..
(You will observe that 9 times 41 is 369 and 9 times 271 is 2439)
Cyclic number 02439 (5digits) had with it 7 other subsidiary cyclic numbers of 5 digits .All these 8 cyclic numbers made it possible to have cyclic formations of 02439 due to multiplication of the same by all the 40 numbers from 1 to 40.
In the case of 271,there are 270 numbers from 1 to 270 for multiplication.So you need 54 cyclic numbers each of 5 digits and hence there are 53 additional (subsidiary) cyclic numbers all multiples of the main one viz 00369. Showing all of them is not going to be easy.So I will show only a few examples-with the suffix M relating to the number by which 00369 is multiplied.
M-1 is 00369.This has cyclic formations of 03690,36900,69003 and 90036 involving M-10,M-100,M-187 and M-244.
This has relationship with cyclic formations 99630,96309,63099,30996 and 09963 involving M-270,M-261,M-171,M-84 and M-27.By relationship I mean the cyclic numbers add up to 99999 and the multiplying numbers add up to 271..-For example 69003+30996=99999 and 187+84=271etc
Another pair of cyclic numbers and cyclic formations----08856(M-24)...88560(M-240),85608(M-232),56088(M-152) 60885(M-165) and...91143(M-247),11439(M-31),14391(M-39),43911(M-119),39114(M-106)...60885+39114=99999 and 165+106=271 etc.
We will thus have 27 pairs having such relationships.
Another pair relates to M values 17,170,74,198,83 and 254,101,197,73 ,188.-..M-17 is 06273 and M-254 is 93726.
Readers may if they like find the other 24 pairs.
I am now presenting details about another 5 digit cyclic number 00369 from 271 operating as the generator..
(You will observe that 9 times 41 is 369 and 9 times 271 is 2439)
Cyclic number 02439 (5digits) had with it 7 other subsidiary cyclic numbers of 5 digits .All these 8 cyclic numbers made it possible to have cyclic formations of 02439 due to multiplication of the same by all the 40 numbers from 1 to 40.
In the case of 271,there are 270 numbers from 1 to 270 for multiplication.So you need 54 cyclic numbers each of 5 digits and hence there are 53 additional (subsidiary) cyclic numbers all multiples of the main one viz 00369. Showing all of them is not going to be easy.So I will show only a few examples-with the suffix M relating to the number by which 00369 is multiplied.
M-1 is 00369.This has cyclic formations of 03690,36900,69003 and 90036 involving M-10,M-100,M-187 and M-244.
This has relationship with cyclic formations 99630,96309,63099,30996 and 09963 involving M-270,M-261,M-171,M-84 and M-27.By relationship I mean the cyclic numbers add up to 99999 and the multiplying numbers add up to 271..-For example 69003+30996=99999 and 187+84=271etc
Another pair of cyclic numbers and cyclic formations----08856(M-24)...88560(M-240),85608(M-232),56088(M-152) 60885(M-165) and...91143(M-247),11439(M-31),14391(M-39),43911(M-119),39114(M-106)...60885+39114=99999 and 165+106=271 etc.
We will thus have 27 pairs having such relationships.
Another pair relates to M values 17,170,74,198,83 and 254,101,197,73 ,188.-..M-17 is 06273 and M-254 is 93726.
Readers may if they like find the other 24 pairs.
No comments:
Post a Comment