A117739 Decimal expansion of the largest C_0 = 1.2209864... such that for C < C_0 and A < 2 the sequence a(n) = floor[A^(C^n)] can't contain only prime terms.

1, 2, 2, 0, 9, 8, 6, 4, 0, 7, 1, 3, 9, 5, 5, 0, 2, 4, 4, 2, 7, 3, 7, 0, 1, 4, 5, 1, 8, 8, 3, 5, 5, 8, 1, 4, 1, 6, 4, 6, 2, 4, 7, 5, 4, 0, 6, 0, 2, 9, 3, 8, 4, 4, 4, 7, 9, 1, 9, 7, 2, 9, 2, 5, 3, 7, 5, 1, 0, 3, 8, 7, 9, 7, 4, 6, 0, 0, 9, 1, 9, 1, 0, 3, 4, 2

Offset

1,2

Comments

It is not proved that for C > C_0 the mentioned infinite sequence of primes actually exists. However, heuristics show that A243358 could be infinite (the decimal expansion of corresponding A value is A243370).

Links

Andrey V. Kulsha, Table of n, a(n) for n = 1..50000

Chris K. Caldwell, A proof of a generalization of Mills' Theorem

Formula

C_0 can be estimated as (logP/log84)^(1/k), where P is k+10th term of A243358.

Crossrefs

Cf. A243358 (primes), A243370 (value of A), A051021 (Mills' constant)

Sequence in context: A079194 A179198 A372390 * A243203 A268652 A111810

Adjacent sequences: A117736 A117737 A117738 * A117740 A117741 A117742

Keyword

nonn,cons

Author

Martin Raab, May 04 2006

Extensions

Terms after a(18) from Andrey V. Kulsha, Jun 03 2014

Status

approved