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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 Rémy Sigrist, Illustration for n = 13 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.)