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A076228
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Start iteration of Collatz-function[A006370] with initial value of n. a[n] shows how many times during fixed-point-list, the value sinks below initial one until reaching endpoint=1.
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1
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0, 1, 2, 2, 3, 5, 4, 3, 6, 5, 6, 8, 6, 9, 6, 4, 8, 13, 10, 7, 5, 11, 8, 10, 13, 9, 9, 15, 13, 10, 9, 5, 16, 11, 8, 19, 17, 16, 17, 8, 12, 7, 19, 15, 13, 11, 12, 11, 19, 20, 17, 11, 9, 17, 14, 19, 23, 18, 21, 15, 13, 16, 14, 6, 22, 24, 21, 14, 12, 11, 15, 22, 18, 21, 7, 21, 19, 25, 22, 9
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| It is believed that for each x a[n]=x occurs finite times and the largest n is 2^x.
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EXAMPLE
| n=18:iteration list={18, 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1}. a[18]= 13 because 13 terms is smaller than iv=18; namely: {9, 14, 7, 11, 17, 13, 10, 5, 16, 8, 4, 2, 1}.
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MATHEMATICA
| f[x_] := (1-Mod[x, 2])*(x/2)+(Mod[x, 2])*(3*x+1) f[1]=1; f0[x_] := Delete[FixedPointList[f, x], -1] f1[x_] := f0[x]-Part[f0[x], 1] f2[x_] := Count[Sign[f1[x]], -1] Table[f2[w], {w, 1, 256}]
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CROSSREFS
| Cf. A006370, A074473.
Sequence in context: A132403 A113167 A036014 * A026408 A036716 A026399
Adjacent sequences: A076225 A076226 A076227 * A076229 A076230 A076231
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Oct 01 2002
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