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

Author

Martin Raab, May 04 2006

Keywords

• nonn
• cons

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

Crossrefs

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

Formula

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

Extensions

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