A260849 Decimal expansion of the maximum performance (operations per second) of an "ultimate laptop".

5, 4, 2, 5, 5, 6, 9, 9, 5, 8, 6, 0, 8, 5, 2, 8, 4, 0, 5, 0, 3, 0, 5, 4, 4, 3, 8, 6, 8, 5, 6, 5, 1, 4, 0, 3, 7, 9, 6, 2, 6, 0, 7, 4, 4, 3, 8, 7, 0, 7, 8, 3, 6, 4, 9, 9, 4, 3, 7, 0, 0, 0, 3, 7, 6, 4, 5, 9, 9, 4, 4, 3, 6, 0, 8, 3, 6, 5, 6, 6, 1, 5, 0, 7, 5, 2, 2, 6, 7, 5, 4, 1, 2, 6, 6, 5, 2, 2, 8, 1

Offset

51,1

Comments

The "ultimate laptop" is a hypothetical computer formed by compressing a kilogram of matter into a black hole the size of its Schwarzschild radius.

Every physical system holds binary digits in the states of its particles. "Computation" makes changes in those states. A system with average energy E can perform a maximum of 2 * E / (Pi * A254181) logical operations per second. The "ultimate laptop" turns all of its matter into energy.

Bremermann's limit gives an even tighter bound of 1.35639... * 10^50 operations per second if the laptop is self-contained. - Charles R Greathouse IV, Apr 18 2016

Links

Table of n, a(n) for n=51..150.

Seth Lloyd, Ultimate physical limits to computation Nature, 406 (2000), 1047-1054; arXiv:quant-ph/9908043, 1999-2000.

Wikipedia, Black hole

Wikipedia, Limits of computation

Formula

Equals 2 * (1 kg) * A182999 / (Pi * A254181).

Example

5.4255699...*10^50 operations per second.

Crossrefs

Cf. A070058, A182999, A254181.

Sequence in context: A309442 A213205 A094778 * A246746 A180131 A257972

Adjacent sequences: A260846 A260847 A260848 * A260850 A260851 A260852

Keyword

nonn,cons

Author

Arkadiusz Wesolowski, Aug 01 2015

Extensions

Edited and extended using modern definitions of fundamental constants by Andrey Zabolotskiy, Apr 22 2023

Status

approved