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A323424 Number of cycles (mod n) under Collatz map. 1
1, 1, 2, 1, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 4, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 3, 3, 2, 3, 2, 4, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 4, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 2, 4, 2, 2, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This sequence is likely to be unbounded.

LINKS

Table of n, a(n) for n=1..87.

Rémy Sigrist, Illustration for n = 13

Index entries for sequences related to 3x+1 (or Collatz) problem

FORMULA

a(n) >= 2 for any n > 4 (as we have at least the cycles (0) and (1, 4, 2)).

EXAMPLE

The initial terms, alongside the corresponding cycles, are:

  n   a(n)  cycles

  --  ----  --------------------

   1     1  (0)

   2     1  (0)

   3     2  (0), (1)

   4     1  (0)

   5     2  (0), (1, 4, 2)

   6     2  (0), (1, 4, 2)

   7     3  (0), (1, 4, 2), (3)

   8     2  (0), (1, 4, 2)

   9     2  (0), (1, 4, 2)

  10     2  (0), (1, 4, 2)

  11     3  (0), (1, 4, 2), (5)

  12     2  (0), (1, 4, 2)

  13     3  (0), (1, 4, 2), (3, 10, 5)

  14     2  (0), (1, 4, 2)

  15     3  (0), (1, 4, 2), (7)

  16     2  (0), (1, 4, 2)

  17     2  (0), (1, 4, 2)

  18     2  (0), (1, 4, 2)

  19     3  (0), (1, 4, 2), (9)

  20     2  (0), (1, 4, 2)

PROG

(PARI) a(n, f = k -> if (k%2, 3*k+1, k/2)) = { my (c=0, s=0); for (k=0, n-1, if (!bittest(s, k), my (v=0, i=k); while (1, v += 2^i; i = f(i) % n; if (bittest(s, i), break, bittest(v, i), c++; break)); s += v)); return (c) }

CROSSREFS

See A000374, A023135, A023153, A233521 for similar sequences.

Cf. A006370.

Sequence in context: A304486 A188550 A064122 * A334098 A263922 A057526

Adjacent sequences:  A323421 A323422 A323423 * A323425 A323426 A323427

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Jan 14 2019

STATUS

approved

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Last modified January 22 05:19 EST 2022. Contains 350481 sequences. (Running on oeis4.)