A364936 a(n) = minimum number of variables with n possible states in a system such that its solution requires the processing of a transcomputational number of bits.

309, 195, 155, 134, 120, 111, 103, 98, 93, 90, 87, 84, 82, 80, 78, 76, 75, 73, 72, 71, 70, 69, 68, 67, 66, 65, 65, 64, 63, 63, 62, 62, 61, 61, 60, 60, 59, 59, 59, 58, 58, 57, 57, 57, 56, 56, 56, 56, 55, 55

Offset

2,1

Comments

The number 10^93, known as Bremermann's limit, is the estimated maximum number of bits able to be processed by a hypothetical Earth-sized computer in a period of time equal to the rough estimate of the Earth's age. All numbers greater than Bremermann's limit are labeled as "transcomputational."

References

H. J. Bremermann, "Optimization through evolution and recombination" in Self-Organizing Systems, Spartan Books, 1962, pages 93-106.

G. J. Klir, Facets of Systems Science, Springer, 1991, pages 121-128.

Links

Table of n, a(n) for n=2..51.

H. J. Bremermann, Optimization through evolution and recombination

Wikipedia, Transcomputational problem

Formula

a(n) = ceiling(93*log(10)/log(n)).

Example

For k = 2 (i.e., a set of n Boolean variables), 309 is the corresponding term of this sequence as it is the smallest integer which satisfies 10^93 < 2^n.

Mathematica

Table[Ceiling[93 Log[10] / Log[n]], {n, 2, 51}]

Crossrefs

Sequence in context: A343273 A337955 A091552 * A159004 A031782 A060980

Adjacent sequences: A364933 A364934 A364935 * A364937 A364938 A364939

Keyword

nonn,easy

Author

Nicholas Leonard, Aug 13 2023

Status

approved