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| A120229
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Split-floor-multiplier sequence (SFMS) using multipliers 1/3 and 3. The SFMS using multipliers r and s is here introduced: for every positive integer n and positive real number r, let [rn] abbreviate floor(rn). Then SFMS(r, s), where max {r, s} > 1, is the sequence a defined by a(n)=[rn] if [rn] > 0 and is not already in a and a(n) = [sn] otherwise.
(history;
published version)
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#19 by Olivier Gérard at Sun Jan 15 01:54:40 EST 2023
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#18 by Olivier Gérard at Sun Jan 15 01:53:52 EST 2023
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| REFERENCES
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Responses to message "Murthy's sequence A073675" to the seqfan(AT)ext.jussieu.fr mailing list. The message and responses are dated Feb 02 2006 and relate to generalizations and properties of sequence A073675, which is SFMS(1/2,2).
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| LINKS
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<a href="http://list.seqfan.eu/oldermail/seqfan-old/2006-February/007226.html">Seqfan: about Murthy's sequence A073675 (1)</a>
<a href="http://list.seqfan.eu/oldermail/seqfan-old/2006-February/007228.html">Seqfan: about Murthy's sequence A073675 (2)</a>
<a href="http://list.seqfan.eu/oldermail/seqfan-old/2006-February/007232.html">Seqfan: about Murthy's sequence A073675 (3)</a>
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| STATUS
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approved
editing
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#17 by Sean A. Irvine at Sat Mar 28 15:50:20 EDT 2020
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#16 by Michel Marcus at Fri Mar 06 01:06:11 EST 2020
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#15 by Jon E. Schoenfield at Thu Mar 05 19:46:04 EST 2020
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#14 by Jon E. Schoenfield at Thu Mar 05 19:46:01 EST 2020
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| NAME
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Split-floor-multiplier sequence (SFMS) using multipliers 1/3 and 3. The SFMS using multipliers r and s is here introduced: for every positive integer n and positive real number r, let [rn] abbreviate floor(rn). Then SFMS(r, s), where max {r, s}>} > 1, is the sequence a defined by a(n)=[rn] if [rn]>] > 0 and is not already in a and a(n)=[) = [sn] otherwise.
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| FORMULA
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a(n)=[) = [n/3] if this is positive and new, elseotherwise a(n)=3n.
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| EXAMPLE
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a(1)=) = 1*3 because [1/3] is not positive.
a(2)=) = 2*3 because [2/3] is not positive.
a(3)=) = 1=[ = [3*(1/3)].
a(4)=) = 4*3 because [4/3]=] = a(3), not new.
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| STATUS
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reviewed
editing
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#13 by Joerg Arndt at Thu Mar 05 11:04:37 EST 2020
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#12 by Peter Munn at Thu Mar 05 10:29:02 EST 2020
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#11 by Peter Munn at Thu Mar 05 09:46:51 EST 2020
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| LINKS
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<a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
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| STATUS
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approved
editing
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#10 by Michel Marcus at Sun Mar 31 03:44:40 EDT 2019
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