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Search: id:A108712
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| A108712 |
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A fractal sequence, defined by a(2n-1) = A007376(n) (the almost-natural numbers), a(2n) = a(n). |
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1
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| 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 1, 3, 0, 6, 1, 2, 1, 7, 1, 4, 2, 8, 1, 1, 3, 9, 1, 5, 4, 1, 1, 3, 5, 0, 1, 6, 6, 1, 1, 2, 7, 1, 1, 7, 8, 1, 1, 4, 9, 2, 2, 8, 0, 1, 2, 1, 1, 3, 2, 9, 2, 1, 2, 5, 3, 4, 2, 1, 4, 1, 2, 3, 5, 5, 2, 0, 6, 1, 2, 6, 7, 6, 2, 1, 8, 1, 2, 2, 9, 7, 3, 1, 0, 1, 3, 7, 1
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Start saying "1" and erase, as soon as they appear, the digits spelling the natural numbers. The result is the sequence itself.
Sequence based on the same skeleton as A108202 (the natural counting digits) but beginning with 1 instead of zero; with n increasing, the apparent correlation between the two sequences disappears.
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LINKS
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Clark Kimberling, Un. of Evansville, Fractal Sequences.
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FORMULA
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a(2n-1) = A007376(n), a(2n) = a(n).
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EXAMPLE
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Say "1" and erase the first "1", then say "2" and erase the first "2" (leaving all other digits where they are), then say "3" and erase the first "3", etc. When it comes to "10" erase the first "1" and then the closest "0", etc. The digits to erase when the count comes to "16", for example, are next one to another.
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MATHEMATICA
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f[n_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = 9i*10^(i - 1) + l; i++ ]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + 10^(i - 1); If[p != 0, IntegerDigits[q][[p]], Mod[q - 1, 10]]]; a[n_] := a[n] = If[EvenQ[n], a[n/2], f[(n + 1)/2]]; Table[ a[n], {n, 105}] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 24 2005)
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CROSSREFS
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a(n)=A108202(n) + 1.
Cf. A003602.
Sequence in context: A003960 A124223 A094193 this_sequence A003602 A049773 A123021
Adjacent sequences: A108709 A108710 A108711 this_sequence A108713 A108714 A108715
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KEYWORD
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base,easy,nonn,nice
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AUTHOR
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Eric Angelini (eric.angelini(AT)kntv.be), Jun 20 2005
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EXTENSIONS
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Additional comments from Robert G. Wilson v (rgwv(AT)rgwv.com) and Alexandre Wajnberg (alexandre.wajnberg(AT)ulb.ac.be), Jun 24 2005
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