

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.


4



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
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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: A184011 A079194 A179198 * 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



