%I #18 Apr 03 2023 10:36:11

%S 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,

%T 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,

%U 0,3,8,7,9,7,4,6,0,0,9,1,9,1,0,3,4,2

%N 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.

%C 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).

%H Andrey V. Kulsha, <a href="/A117739/b117739.txt">Table of n, a(n) for n = 1..50000</a>

%H Chris K. Caldwell, <a href="https://t5k.org/notes/proofs/A3n.html">A proof of a generalization of Mills' Theorem</a>

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

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

%K nonn,cons

%O 1,2

%A _Martin Raab_, May 04 2006

%E Terms after a(18) from _Andrey V. Kulsha_, Jun 03 2014