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A269572 Maximal period-length associated with binary fractility of n. 2
1, 1, 1, 2, 1, 2, 1, 3, 2, 5, 1, 6, 2, 3, 1, 4, 3, 9, 2, 4, 5, 7, 1, 10, 6, 9, 2, 14, 3, 4, 1, 5, 4, 7, 3, 18, 9, 8, 2, 10, 4, 7, 5, 7, 7, 14, 1, 11, 10, 6, 6, 26, 9, 12, 2, 9, 14, 29, 3, 30, 4, 5, 1, 6, 5, 33, 4, 11, 7, 21, 3, 6, 18, 11, 9, 15, 8, 22, 2, 27 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,4

COMMENTS

For each x in (0,1], let 1/2^p(1) + 1/2^p(2) + ... be the infinite binary representation of x. Let d(1) = p(1) and d(i) = p(i) - p(i-1) for i >=2. Call (d(i)) the powerdifference sequence of x, and denote it by D(x). Call m/n and u/v equivalent if every period of D(m/n) is a period of D(u/v). Define the binary fractility of n to be the number of distinct equivalence classes of {m/n: 0 < m < n}. Each class is represented by a minimal period, and a(n) is the length of the longest such period.

LINKS

Table of n, a(n) for n=2..81.

EXAMPLE

n        classes          a(n)

2         (1)              1

3         (2)              1

4         (1)              1

5         (1,3)            2

6         (1), (2)         1

7         (1,2), (3)       2

8         (1)              1

9         (1), (1,1,4)     3

10        (1), (1,3)       1

CROSSREFS

Cf. A269570, A269571.

Sequence in context: A226517 A185214 A241719 * A029198 A029175 A186994

Adjacent sequences:  A269569 A269570 A269571 * A269573 A269574 A269575

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 01 2016

STATUS

approved

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Last modified February 27 13:18 EST 2020. Contains 332306 sequences. (Running on oeis4.)