On Weakly Complete Sequences Formed by the Greedy Algorithm
In this article, we consider increasing sequences of positive integers defined in the following manner. Let the initial terms a1 and a2 be given, and for any define to be the smallest integer greater than which cannot be written as a sum of (distinct) previous terms of the sequence. For various p...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Knapp, Michael P. [verfasserIn] Paul, Michael D. [verfasserIn] |
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| Format: |
E-Artikel |
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| Erschienen: |
Walter de Gruyter GmbH & Co. KG ; 2012 |
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| Schlagwörter: |
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| Umfang: |
18 |
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| Reproduktion: |
Walter de Gruyter Online Zeitschriften |
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| Übergeordnetes Werk: |
Enthalten in: Integers - Berlin [u.a.] : de Gruyter, 2009, 12(2012), 4 vom: 01. Aug., Seite 473-490 |
| Übergeordnetes Werk: |
volume:12 ; year:2012 ; number:4 ; day:01 ; month:08 ; pages:473-490 ; extent:18 |
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| DOI / URN: |
10.1515/integers-2011-0118 |
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NLEJ247027472 |
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10.1515/integers-2011-0118 doi artikel_Grundlieferung.pp (DE-627)NLEJ247027472 DE-627 ger DE-627 rakwb Knapp, Michael P. verfasserin aut On Weakly Complete Sequences Formed by the Greedy Algorithm Walter de Gruyter GmbH & Co. KG 2012 18 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this article, we consider increasing sequences of positive integers defined in the following manner. Let the initial terms a1 and a2 be given, and for any define to be the smallest integer greater than which cannot be written as a sum of (distinct) previous terms of the sequence. For various parametrized choices of the initial terms, we determine precisely the terms of the sequences obtained by this method. We also conjecture that for all choices of the initial terms, even in a more general setting, the terms of sequences defined in this manner have interesting patterns. Walter de Gruyter Online Zeitschriften Weakly Complete Sequences Greedy Algorithm Patterns in Sequences Paul, Michael D. verfasserin aut Enthalten in Integers Berlin [u.a.] : de Gruyter, 2009 12(2012), 4 vom: 01. Aug., Seite 473-490 (DE-627)NLEJ248235834 (DE-600)2502663-X 1867-0652 nnns volume:12 year:2012 number:4 day:01 month:08 pages:473-490 extent:18 https://doi.org/10.1515/integers-2011-0118 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 12 2012 4 01 08 473-490 18 |
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10.1515/integers-2011-0118 doi artikel_Grundlieferung.pp (DE-627)NLEJ247027472 DE-627 ger DE-627 rakwb Knapp, Michael P. verfasserin aut On Weakly Complete Sequences Formed by the Greedy Algorithm Walter de Gruyter GmbH & Co. KG 2012 18 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this article, we consider increasing sequences of positive integers defined in the following manner. Let the initial terms a1 and a2 be given, and for any define to be the smallest integer greater than which cannot be written as a sum of (distinct) previous terms of the sequence. For various parametrized choices of the initial terms, we determine precisely the terms of the sequences obtained by this method. We also conjecture that for all choices of the initial terms, even in a more general setting, the terms of sequences defined in this manner have interesting patterns. Walter de Gruyter Online Zeitschriften Weakly Complete Sequences Greedy Algorithm Patterns in Sequences Paul, Michael D. verfasserin aut Enthalten in Integers Berlin [u.a.] : de Gruyter, 2009 12(2012), 4 vom: 01. Aug., Seite 473-490 (DE-627)NLEJ248235834 (DE-600)2502663-X 1867-0652 nnns volume:12 year:2012 number:4 day:01 month:08 pages:473-490 extent:18 https://doi.org/10.1515/integers-2011-0118 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 12 2012 4 01 08 473-490 18 |
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10.1515/integers-2011-0118 doi artikel_Grundlieferung.pp (DE-627)NLEJ247027472 DE-627 ger DE-627 rakwb Knapp, Michael P. verfasserin aut On Weakly Complete Sequences Formed by the Greedy Algorithm Walter de Gruyter GmbH & Co. KG 2012 18 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this article, we consider increasing sequences of positive integers defined in the following manner. Let the initial terms a1 and a2 be given, and for any define to be the smallest integer greater than which cannot be written as a sum of (distinct) previous terms of the sequence. For various parametrized choices of the initial terms, we determine precisely the terms of the sequences obtained by this method. We also conjecture that for all choices of the initial terms, even in a more general setting, the terms of sequences defined in this manner have interesting patterns. Walter de Gruyter Online Zeitschriften Weakly Complete Sequences Greedy Algorithm Patterns in Sequences Paul, Michael D. verfasserin aut Enthalten in Integers Berlin [u.a.] : de Gruyter, 2009 12(2012), 4 vom: 01. Aug., Seite 473-490 (DE-627)NLEJ248235834 (DE-600)2502663-X 1867-0652 nnns volume:12 year:2012 number:4 day:01 month:08 pages:473-490 extent:18 https://doi.org/10.1515/integers-2011-0118 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 12 2012 4 01 08 473-490 18 |
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10.1515/integers-2011-0118 doi artikel_Grundlieferung.pp (DE-627)NLEJ247027472 DE-627 ger DE-627 rakwb Knapp, Michael P. verfasserin aut On Weakly Complete Sequences Formed by the Greedy Algorithm Walter de Gruyter GmbH & Co. KG 2012 18 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this article, we consider increasing sequences of positive integers defined in the following manner. Let the initial terms a1 and a2 be given, and for any define to be the smallest integer greater than which cannot be written as a sum of (distinct) previous terms of the sequence. For various parametrized choices of the initial terms, we determine precisely the terms of the sequences obtained by this method. We also conjecture that for all choices of the initial terms, even in a more general setting, the terms of sequences defined in this manner have interesting patterns. Walter de Gruyter Online Zeitschriften Weakly Complete Sequences Greedy Algorithm Patterns in Sequences Paul, Michael D. verfasserin aut Enthalten in Integers Berlin [u.a.] : de Gruyter, 2009 12(2012), 4 vom: 01. Aug., Seite 473-490 (DE-627)NLEJ248235834 (DE-600)2502663-X 1867-0652 nnns volume:12 year:2012 number:4 day:01 month:08 pages:473-490 extent:18 https://doi.org/10.1515/integers-2011-0118 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 12 2012 4 01 08 473-490 18 |
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10.1515/integers-2011-0118 doi artikel_Grundlieferung.pp (DE-627)NLEJ247027472 DE-627 ger DE-627 rakwb Knapp, Michael P. verfasserin aut On Weakly Complete Sequences Formed by the Greedy Algorithm Walter de Gruyter GmbH & Co. KG 2012 18 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this article, we consider increasing sequences of positive integers defined in the following manner. Let the initial terms a1 and a2 be given, and for any define to be the smallest integer greater than which cannot be written as a sum of (distinct) previous terms of the sequence. For various parametrized choices of the initial terms, we determine precisely the terms of the sequences obtained by this method. We also conjecture that for all choices of the initial terms, even in a more general setting, the terms of sequences defined in this manner have interesting patterns. Walter de Gruyter Online Zeitschriften Weakly Complete Sequences Greedy Algorithm Patterns in Sequences Paul, Michael D. verfasserin aut Enthalten in Integers Berlin [u.a.] : de Gruyter, 2009 12(2012), 4 vom: 01. Aug., Seite 473-490 (DE-627)NLEJ248235834 (DE-600)2502663-X 1867-0652 nnns volume:12 year:2012 number:4 day:01 month:08 pages:473-490 extent:18 https://doi.org/10.1515/integers-2011-0118 Deutschlandweit zugänglich GBV_USEFLAG_U ZDB-1-DGR GBV_NL_ARTICLE AR 12 2012 4 01 08 473-490 18 |
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In this article, we consider increasing sequences of positive integers defined in the following manner. Let the initial terms a1 and a2 be given, and for any define to be the smallest integer greater than which cannot be written as a sum of (distinct) previous terms of the sequence. For various parametrized choices of the initial terms, we determine precisely the terms of the sequences obtained by this method. We also conjecture that for all choices of the initial terms, even in a more general setting, the terms of sequences defined in this manner have interesting patterns. |
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In this article, we consider increasing sequences of positive integers defined in the following manner. Let the initial terms a1 and a2 be given, and for any define to be the smallest integer greater than which cannot be written as a sum of (distinct) previous terms of the sequence. For various parametrized choices of the initial terms, we determine precisely the terms of the sequences obtained by this method. We also conjecture that for all choices of the initial terms, even in a more general setting, the terms of sequences defined in this manner have interesting patterns. |
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In this article, we consider increasing sequences of positive integers defined in the following manner. Let the initial terms a1 and a2 be given, and for any define to be the smallest integer greater than which cannot be written as a sum of (distinct) previous terms of the sequence. For various parametrized choices of the initial terms, we determine precisely the terms of the sequences obtained by this method. We also conjecture that for all choices of the initial terms, even in a more general setting, the terms of sequences defined in this manner have interesting patterns. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">NLEJ247027472</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220820025519.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">220814s2012 xx |||||o 00| ||und c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/integers-2011-0118</subfield><subfield code="2">doi</subfield></datafield><datafield tag="028" ind1="5" ind2="2"><subfield code="a">artikel_Grundlieferung.pp</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)NLEJ247027472</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Knapp, Michael P.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On Weakly Complete Sequences Formed by the Greedy Algorithm</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="b">Walter de Gruyter GmbH & Co. KG</subfield><subfield code="c">2012</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">18</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">In this article, we consider increasing sequences of positive integers defined in the following manner. Let the initial terms a1 and a2 be given, and for any define to be the smallest integer greater than which cannot be written as a sum of (distinct) previous terms of the sequence. For various parametrized choices of the initial terms, we determine precisely the terms of the sequences obtained by this method. We also conjecture that for all choices of the initial terms, even in a more general setting, the terms of sequences defined in this manner have interesting patterns.</subfield></datafield><datafield tag="533" ind1=" " ind2=" "><subfield code="f">Walter de Gruyter Online Zeitschriften</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Weakly Complete Sequences</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Greedy Algorithm</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Patterns in Sequences</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Paul, Michael D.</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Integers</subfield><subfield code="d">Berlin [u.a.] : de Gruyter, 2009</subfield><subfield code="g">12(2012), 4 vom: 01. Aug., Seite 473-490</subfield><subfield code="w">(DE-627)NLEJ248235834</subfield><subfield code="w">(DE-600)2502663-X</subfield><subfield code="x">1867-0652</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:12</subfield><subfield code="g">year:2012</subfield><subfield code="g">number:4</subfield><subfield code="g">day:01</subfield><subfield code="g">month:08</subfield><subfield code="g">pages:473-490</subfield><subfield code="g">extent:18</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/integers-2011-0118</subfield><subfield code="z">Deutschlandweit zugänglich</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_U</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-1-DGR</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_NL_ARTICLE</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">12</subfield><subfield code="j">2012</subfield><subfield code="e">4</subfield><subfield code="b">01</subfield><subfield code="c">08</subfield><subfield code="h">473-490</subfield><subfield code="g">18</subfield></datafield></record></collection>
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