Let the set of all repunits (repeated units) i.e., 1,11,111,... is X.
=> X = { Rn : n belongs to postive integer }
(Repunit of n defined by Rn. 1 is R!. 11 is R2, etc....)
Generally X is not satisfy closed property.
Dear Arunagirinathan,
1. What do you mean under "closed property"? What operation?
2. If k>2 then a necessary condition for R_k to be a prime is that k is itself a prime (R_d divides R_k if d divides k). This condition is not sufficient: Maple calculations show that R_19 and R_23 are primes but R_p are not primes for prime p1 and d divides k.
Best regards, Yuri
Dear Yuri, for R3 , we have 111=3x37
Dear Srinivasan
For the closed property, if you meant closed for an operation, you can take Rn *Rm=Rn Rm here not multiplication but juxtaposition, so, Rn*Rm =Rn+m : for example R1 *R2 =R3
Dear Hanifa,
yes, it is as I said above, among R_3, R_5, ..., R_43 (prime indices) only R_19 and R_23 are also primes. I don't know any sufficient condition for R_p to be a prime (where p is an odd prime).
We have that R_n=(10^n-1)/9. Introduce a new operation * on the set real numbers /
a*b:=ln(1/9*exp(ln(10)*a+ln(10)*b)-1/9*exp(ln(10)*a)-1/9*exp(ln(10)*b)+10/9)/ln(10)
Then
R_a R_b=R_{a*b}
Dear Hanifa Zekraoui,
I thing your operation like concatenation. is it?
Yes dear Srinivasan, put the second "word" just next the first one. In French we call it juxtaposition, I think the terminology is the same in English .
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