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Shapiro mentions on page 30 of his paper the conjecture that a(n) is prime for each n > 1, but a(13) is composite and so the conjecture fails. [_- _Charles R Greathouse IV_, Oct 28 2011]
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Shapiro shows that the smallest number is greater the than 2^(n-1). Catlin shows that if a(n) is odd and composite, then its factors are among the a(k), k < n. For example a(12) = a(5) a(8). There is a conjecture that all terms of this sequence are odd. - T. D. Noe, Mar 08 2004
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T. D. Noe, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL11/Noe/noe080107.html">Primes in classes of the iterated totient function</a>, JIS 11 (2008) 08.1.2
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The indices of odd prime terms are given by n=A136040(k)+2 for k=1,2,3,.... - _T. D. Noe, _, Dec 14 2007
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