{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T00:54:45Z","timestamp":1649206485191},"reference-count":4,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2015]]},"abstract":"<jats:p>The order of appearance<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>z<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>n<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>of the positive integer<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math>is the smallest positive integer<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>k<\/mml:mi><\/mml:mrow><\/mml:math>such that<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math>divides<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:msub><mml:mrow><mml:mi>F<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>k<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>, the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mi>k<\/mml:mi><\/mml:mrow><\/mml:math>th member of the Fibonacci sequence. In this paper, we improve upon some results from (Marques, 2011) concerning local minima of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mi>z<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>n<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>.<\/jats:p>","DOI":"10.1155\/2015\/823973","type":"journal-article","created":{"date-parts":[[2015,10,1]],"date-time":"2015-10-01T17:07:36Z","timestamp":1443719256000},"page":"1-3","source":"Crossref","is-referenced-by-count":0,"title":["On the Local Minima of the Order of Appearance Function"],"prefix":"10.1155","volume":"2015","author":[{"given":"Florian","family":"Luca","sequence":"first","affiliation":[{"name":"School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits, Johannesburg 2050, South Africa"}]},{"given":"Thato","family":"Mosima","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits, Johannesburg 2050, South Africa"}]}],"member":"98","reference":[{"key":"4","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/407643"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1142\/S1793042114500079"},{"issue":"2","key":"2","first-page":"30","volume":"15","year":"1913","journal-title":"Annals of Mathematics"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1515\/crll.2001.080"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2015\/823973.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2015\/823973.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2015\/823973.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,27]],"date-time":"2016-07-27T15:58:23Z","timestamp":1469635103000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2015\/823973\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"references-count":4,"alternative-id":["823973","823973"],"URL":"https:\/\/doi.org\/10.1155\/2015\/823973","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]}}}