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URL: https://oeis.org/A087262

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A087262
Integer quotient of largest and initial values in 3x+1 iteration, started at n.
1
1, 1, 5, 1, 3, 2, 7, 1, 5, 1, 4, 1, 3, 3, 10, 1, 3, 2, 4, 1, 3, 2, 6, 1, 3, 1, 341, 1, 3, 5, 297, 1, 3, 1, 4, 1, 3, 2, 7, 1, 225, 1, 4, 1, 3, 3, 196, 1, 3, 1, 4, 1, 3, 170, 167, 1, 3, 1, 5, 2, 3, 148, 146, 1, 3, 1, 4, 1, 3, 2, 130, 1, 126, 1, 4, 1, 3, 3, 10, 1, 3, 112, 111, 1, 3, 2, 6, 1, 3, 1, 101
OFFSET
1,3
COMMENTS
Remarkably often, several consecutive terms are identical or close, showing closeness of peaks too: at n=107-111, a(n)=83-86.
If a(n)=1, then the peak is the start-value (per A166245).
It is conjectured that if peak/initial value is an integer then it equals 1.
FORMULA
a(n) = floor(A025586(n)/n).
MATHEMATICA
c[x_] := (1-Mod[x, 2])*(x/2)+Mod[x, 2]*(3*x+1)c[1]=1; fpl[x_] := Delete[FixedPointList[c, x], -1] Table[Floor[Max[fpl[w]]/w//N], {w, 1, 256}]
CROSSREFS
Cf. A025586, A056959, A166245 (indices of 1's).
Sequence in context: A068237 A373363 A083345 * A082343 A166125 A199074
KEYWORD
nonn
AUTHOR
Labos Elemer, Sep 11 2003
STATUS
approved