Define a sequence $latex a_0$, $latex a_1$, $latex a_2$, $latex \\ldots$ of integers as follows:<\/p>\n
$latex a_0=0$, and given $latex a_0$, $latex a_1$, $latex a_2$, $latex \\ldots$, $latex a_n$, then $latex a_{n+1}$ is the least integer greater than $latex a_n$ such that no three distinct terms (not necessarily consecutive) of $latex a_0$, $latex a_1$, $latex a_2$, $latex \\ldots$, $latex a_{n+1}$ are in arithmetic progression. (This means that for no $latex 0\\leq i < j < k \\leq n+1$ do we have $latex a_j – a_i = a_k – a_j$.)<\/p>\n
Find a simple rule for determining $latex a_n$. For instance, what is $latex a_{1000000}$? The sequence begins $latex 0$, $latex 1$, $latex 3$, $latex 4$, $latex 9$, $latex 10$, $latex 12$, $latex \\ldots$.<\/p>\n
Due day is May 3.<\/p>\n","protected":false},"excerpt":{"rendered":"
Define a sequence $latex a_0$, $latex a_1$, $latex a_2$, $latex \\ldots$ of integers as follows: $latex a_0=0$, and given $latex a_0$, $latex a_1$, $latex a_2$, $latex \\ldots$, $latex a_n$, then $latex a_{n+1}$ is the least integer greater than $latex a_n$… <\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"_links":{"self":[{"href":"https:\/\/mathcs.ksa.hs.kr\/index.php?rest_route=\/wp\/v2\/posts\/2005"}],"collection":[{"href":"https:\/\/mathcs.ksa.hs.kr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathcs.ksa.hs.kr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathcs.ksa.hs.kr\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/mathcs.ksa.hs.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2005"}],"version-history":[{"count":6,"href":"https:\/\/mathcs.ksa.hs.kr\/index.php?rest_route=\/wp\/v2\/posts\/2005\/revisions"}],"predecessor-version":[{"id":2011,"href":"https:\/\/mathcs.ksa.hs.kr\/index.php?rest_route=\/wp\/v2\/posts\/2005\/revisions\/2011"}],"wp:attachment":[{"href":"https:\/\/mathcs.ksa.hs.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2005"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathcs.ksa.hs.kr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2005"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathcs.ksa.hs.kr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2005"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}