# Von Neumann Exponent Calculator

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This Demonstration was inspired by a passage in Sylvia Nasar's book, *A Beautiful Mind, The Life of Mathematical Genius and Nobel Laureate John Nash*, (Touchstone Edition, 2001). Page 80 of that book relates an anecdote about John von Neumann's ability to divine by inspection the smallest integral power of 2 in which a specified integer was at a given position, counting from either left or right. Let the *von Neumann exponent* be the smallest integer so that contains the target digit in the specified position. This exercise performs that computation, reporting the exponent , the power , and the target integer highlighted in yellow.

Contributed by: Daniel G. Martinez (March 2011)

Additional contributions by: Oleksandr Pavlyk

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

To work with variations on the theme of target integer position in integral power expressions, change the base in the program from 2 to other integers greater than zero and construct tables that evaluate the module over various domains. The program used to develop this Demonstration has vast potential for research applications in *A New Kind of Science*.

The position begins at 2 in order to eliminate the potential of attempting to find zero as a leading integer in a power of 2. You can set the position iterator in this Demonstration arbitrarily high, but that might require additional formatting work for large values.

The term *von Neumann exponent* was minted for this Demonstration's narrative and is not intended to represent a formal mathematical concept.

## Permanent Citation

"Von Neumann Exponent Calculator"

http://demonstrations.wolfram.com/VonNeumannExponentCalculator/

Wolfram Demonstrations Project

Published: March 7 2011