On binary representations of integers with digits .

Prodinger, Helmut

Displaying similar documents to “On binary representations of integers with digits $- 1, 0, 1$ .”

Signed bits and fast exponentiation

Wieb Bosma (2001)

Journal de théorie des nombres de Bordeaux

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An exact analysis is given of the benefits of using the non-adjacent form representation for integers (rather than the binary representation), when computing powers of elements in a group in which inverting is easy. By counting the number of multiplications for a random exponent requiring a given number of bits in its binary representation, we arrive at a precise version of the known asymptotic result that on average one in three signed bits in the non-adjacent form is non-zero. This...

Generating functions for the digital sum and other digit counting sequences.

Adams-Watters, Franklin T., Ruskey, Frank (2009)

Journal of Integer Sequences [electronic only]

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An exercise on Fibonacci representations

Jean Berstel (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We give a partial answer to a question of Carlitz asking for a closed formula for the number of distinct representations of an integer in the Fibonacci base.