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Smallest prime p such that n applications of f lead form p to 2, where f is the mapping of primes > 2 to primes defined by A052248.
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%I #4 Mar 30 2012 17:27:40

%S 2,3,5,7,13,23,43,83,163,317,631,1259,2503,5003,9973,19937,39869,

%T 119617,239233,480023,960031,1920049,3840091,7680181,15360361,

%U 30720719,61441379,122882741,245765449,491530873,983061713,1966123417

%N Smallest prime p such that n applications of f lead form p to 2, where f is the mapping of primes > 2 to primes defined by A052248.

%C RECORDS transform of A080189; prime p sets a new record for the number of applications of f that are required to reach 2. - a(n) = prime preceding 2*a(n-1) as long as a(n-1) is a term of A080191; if however a(n-1) is a term of A080192, then a(n) > 2*a(n-1). - Next term a(32) > 3932600000, presumably a(32) = 5274863189, a(33) = 10549726367. - The sequence coincides with A006992 (Bertrand primes: a(n) is largest prime < 2*a(n-1)) for the first 17 terms; first divergence occurs after term 39869 because this is the first term which belongs to A080192.

%F f^n(p) = 2.

%e f(23) = 13, f(13) = 7, f(7) = 5, f(5) = 3, f(3) = 2; five applications of f are required to reach 2 and for all primes < 23 at most four applications are required, so a(5) = 23.

%Y Cf. A052248, A080189, A080191, A080192, A006992.

%K nonn

%O 0,1

%A _Klaus Brockhaus_, Feb 10 2003