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Iterates of A014580, starting with a(0) = 1, a(n) = A014580^(n)(1). [Here A014580^(n) means the n-th fold application of A014580].
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%I #30 Aug 08 2014 08:59:18

%S 1,2,3,7,25,137,1123,13103,204045,4050293,99440273

%N Iterates of A014580, starting with a(0) = 1, a(n) = A014580^(n)(1). [Here A014580^(n) means the n-th fold application of A014580].

%H A. Karttunen, <a href="/A091247/a091247.scm.txt">Scheme-program for computing this sequence.</a>

%H <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>

%F a(0)=1, a(n) = A014580(a(n-1)). [The defining recurrence].

%F From _Antti Karttunen_, Aug 03 2014: (Start)

%F Other identities. For all n >= 0, the following holds:

%F A091238(a(n)) = n+1.

%F a(n) = A091204(A007097(n)) and A091205(a(n)) = A007097(n).

%F a(n) = A245703(A007097(n)) and A245704(a(n)) = A007097(n).

%F a(n) = A245702(A000079(n)) and A245701(a(n)) = A000079(n).

%F (End)

%o (PARI)

%o isA014580(n)=polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from _Charles R Greathouse IV_

%o prev=1; i=0; print1(1, ", "); for(n=1, 123456789, if(isA014580(n), i++; if((i == prev), print1(n, ", "); prev=n))) \\ _Antti Karttunen_, Aug 02 2014

%Y Cf. A000079, A007097, A091238, A091204-A091205, A245701-A245702, A245703-A245704.

%K nonn

%O 0,2

%A _Antti Karttunen_, Jan 03 2004

%E Terms a(8)-a(10) computed by _Antti Karttunen_, Aug 02 2014