{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T19:35:40Z","timestamp":1776800140098,"version":"3.51.2"},"reference-count":15,"publisher":"American Mathematical Society (AMS)","issue":"297","license":[{"start":{"date-parts":[[2016,6,15]],"date-time":"2016-06-15T00:00:00Z","timestamp":1465948800000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00c3\u00adfico y Tecnol\u00c3\u00b3gico","doi-asserted-by":"publisher","award":["11100260"],"award-info":[{"award-number":["11100260"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We prove that for each odd number\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k\">\n                        <mml:semantics>\n                          <mml:mi>k<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    , the sequence\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"left-parenthesis k 2 Superscript n Baseline plus 1 right-parenthesis Subscript n greater-than-or-equal-to 1\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mo stretchy=\"false\">(<\/mml:mo>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:msup>\n                              <mml:mn>2<\/mml:mn>\n                              <mml:mi>n<\/mml:mi>\n                            <\/mml:msup>\n                            <mml:mo>+<\/mml:mo>\n                            <mml:mn>1<\/mml:mn>\n                            <mml:msub>\n                              <mml:mo stretchy=\"false\">)<\/mml:mo>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mi>n<\/mml:mi>\n                                <mml:mo>\n                                  \u2265\n                                  \n                                <\/mml:mo>\n                                <mml:mn>1<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">(k2^n+1)_{n\\ge 1}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    contains only a finite number of Carmichael numbers. We also prove that\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k equals 27\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mn>27<\/mml:mn>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">k=27<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is the smallest value for which such a sequence contains some Carmichael number.\n                  <\/p>","DOI":"10.1090\/mcom\/2982","type":"journal-article","created":{"date-parts":[[2015,6,15]],"date-time":"2015-06-15T08:53:56Z","timestamp":1434358436000},"page":"357-377","source":"Crossref","is-referenced-by-count":4,"title":["Carmichael numbers in the sequence (2\u207f\ud835\udc58+1)_{\ud835\udc5b\u22651}"],"prefix":"10.1090","volume":"85","author":[{"given":"Javier","family":"Cilleruelo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Florian","family":"Luca","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amalia","family":"Pizarro-Madariaga","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,6,15]]},"reference":[{"issue":"3","key":"1","doi-asserted-by":"publisher","first-page":"703","DOI":"10.2307\/2118576","article-title":"There are infinitely many Carmichael numbers","volume":"139","author":"Alford, W. R.","year":"1994","journal-title":"Ann. of Math. (2)","ISSN":"https:\/\/id.crossref.org\/issn\/0003-486X","issn-type":"print"},{"key":"2","unstructured":"W. D. Banks, C. E. Finch, F. Luca, C. Pomerance and P. St\u0103nic\u0103, Sierpi\u0144ski and Carmichael numbers, Preprint, 2012."},{"issue":"1","key":"3","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/s00209-002-0449-z","article-title":"An upper bound for the G.C.D. of \ud835\udc4e\u207f-1 and \ud835\udc4f\u207f-1","volume":"243","author":"Bugeaud, Yann","year":"2003","journal-title":"Math. 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