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Old 2019-06-26, 19:45   #17
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"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

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Originally Posted by R. Gerbicz View Post
The common generalization could be:
a(n)=polcyclo(h*n,2) for fixed h>0 integer.
For h=1 a(a(p))=M(M(p)) if p and M(p)=2^p-1 is prime.
For h=2 a(a(p))=W(W(p)) if p and W(p)=(2^p+1)/3 is prime.
And you can see this for h>2 also.

Or you can even drop the n=p requirement (ofcourse in this case a(n)!=M(n) for h=1 etc.),
note that we can see a(n)=prime or a(a(n))=prime for composite n values also.
The common generalization is Phi(Phi(n,2),2) and Phi(2*Phi(n,2),2), with any integer n

However, there are no known n such that Phi(n,2) is composite but Phi(Phi(n,2),2) is prime, also no known n such that Phi(n,2) is composite but Phi(2*Phi(n,2),2) is prime

Last fiddled with by sweety439 on 2019-06-26 at 19:51
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