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.

2, 3, 5, 7, 13, 23, 43, 83, 163, 317, 631, 1259, 2503, 5003, 9973, 19937, 39869, 119617, 239233, 480023, 960031, 1920049, 3840091, 7680181, 15360361, 30720719, 61441379, 122882741, 245765449, 491530873, 983061713, 1966123417

Offset: 0

Author

Klaus Brockhaus, Feb 10 2003

Keywords

• nonn

Comments

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.

Examples

			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.
		

Crossrefs

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

Formula

f^n(p) = 2.