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Search: id:A076227
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| A076227 |
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Iteration of Collatz function starts with initial value chosen from some residue class Modulo 2^n. If r remainder (of initial value) is fixed, i.e. m=i.v=(2^n)k+r, then A074473[m] may be independent of k, or it may be dependent. Terms of this sequence provide the number of those residue classes in which A074473(m) is not constant, i.e. when it depends on k. |
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1
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| 1, 1, 2, 3, 4, 8, 13, 19, 38, 64, 128, 226, 367, 734, 1295, 2114
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OFFSET
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1,3
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COMMENT
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The ratio of numbers of inhomogenous r-classes versus uniform-classes enumerated here increases with n and tends to 0. For n large enough ratio < a[16]/65536=2114/65536 ~ 3.23 per cent.
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FORMULA
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a(n)= number of residue classes in which A074473[m] is not constant.
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EXAMPLE
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n=6: Modulo 64, eight residue classes were counted: r=7, 15, 27, 31, 39, 47, 59, 63. See A075476-A075483. For other 64-8=56 r-classes u[q]=A074473[64k+q] is constant: in 32 class u[q]=2, in 16 classes u[q]=4, in 4 classes u[q]=7 and in 4 cases u[q]=9. E.g. for r=11, 23, 43, 55 A047473[64k+r]=9 independently of k.
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CROSSREFS
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Cf. A006370, A074473, A075476-A075483.
Sequence in context: A034776 A068791 A126042 this_sequence A092075 A091415 A166342
Adjacent sequences: A076224 A076225 A076226 this_sequence A076228 A076229 A076230
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KEYWORD
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more,nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Oct 01 2002
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