This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A080190 #4 Mar 30 2012 17:27:40 %S A080190 2,3,5,7,13,23,43,83,163,317,631,1259,2503,5003,9973,19937,39869, %T A080190 119617,239233,480023,960031,1920049,3840091,7680181,15360361, %U A080190 30720719,61441379,122882741,245765449,491530873,983061713,1966123417 %N A080190 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 A080190 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 A080190 f^n(p) = 2. %e A080190 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 A080190 Cf. A052248, A080189, A080191, A080192, A006992. %K A080190 nonn %O A080190 0,1 %A A080190 _Klaus Brockhaus_, Feb 10 2003