A364936 - OEIS

%I #8 Sep 03 2023 11:21:41

%S 309,195,155,134,120,111,103,98,93,90,87,84,82,80,78,76,75,73,72,71,

%T 70,69,68,67,66,65,65,64,63,63,62,62,61,61,60,60,59,59,59,58,58,57,57,

%U 57,56,56,56,56,55,55

%N 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.

%C 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."

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

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

%H H. J. Bremermann, <a href="https://holtz.org/Library/Natural%20Science/Physics/Optimization%20Through%20Evolution%20and%20Recombination%20-%20Bremermann%201962.htm">Optimization through evolution and recombination</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Transcomputational_problem">Transcomputational problem</a>

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

%e 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.

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

%K nonn,easy

%O 2,1

%A _Nicholas Leonard_, Aug 13 2023