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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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified January 18 13:09 EST 2019. Contains 319271 sequences. (Running on oeis4.)