40 citations · 73 across the 13 of their papers we have counts for
6 papers · 1 filter
The Yellowstone Permutation
David L. Applegate, Hans Havermann, Bob Selcoe +3
Define a sequence of positive integers by the rule that a(n) = n for 1 <= n <= 3, and for n >= 4, a(n) is the smallest number not already in the sequence which has a common factor…
Dismal Arithmetic
David Applegate, Marc LeBrun, N. J. A. Sloane
Dismal arithmetic is just like the arithmetic you learned in school, only simpler: there are no carries, when you add digits you just take the largest, and when you multiply digits…
Descending Dungeons and Iterated Base-Changing
David Applegate, Marc LeBrun, N. J. A. Sloane
For real numbers a, b> 1, let as a_b denote the result of interpreting a in base b instead of base 10. We define ``dungeons'' (as opposed to ``towers'') to be numbers of the form a…
Sloping Binary Numbers: A New Sequence Related to the Binary Numbers
David Applegate, Benoit Cloitre, Philippe Deléham +1
If the list of binary numbers is read by upward-sloping diagonals, the resulting ``sloping binary numbers'' 0, 11, 110, 101, 100, 1111, 1010, ... (or 0, 3, 6, 5, 4, 15, 10, ...) ha…
The 3x+1 Semigroup
David Applegate, Jeffrey C. Lagarias
The 3x+1 semigroup is the multiplicative semigroup generated by the rational numbers of form (2k+1)/(3k+2) for non-negative k, together with 2. This semigroup encodes backward iter…
Lower bounds for the total stopping time of 3X+1 iterates
David Applegate, Jeffrey C. Lagarias
The 3X+1 function T(n) is (3n+1)/2 if n is odd and n/2 if n is even. The total stopping time σ_\infty (n) for a positive integer n is the number of iterations of the 3x+1 function…