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

Author

Nicholas Leonard, Aug 13 2023

Keywords

• nonn
• easy

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."

Examples

			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.
		

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

• H. J. Bremermann, Optimization through evolution and recombination
• Wikipedia, Transcomputational problem

Programs

Mathematica

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

Formula

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