Re: [math-fun] Add to n its second smallest non-divider. Loop
Could please someone compute a few terms more of: < Add to n the n-th smallest number not dividing n > (this is a kind of self-generalization of the rule herunder) I've found this first few terms: S = 1,3,8,20,46,96,... Best, É. (not in the OEIS though 1,3,8,20,46 gives 4 hits) -----Message d'origine----- De : Eric Angelini [mailto:Eric.Angelini@kntv.be] Envoyé : mercredi 25 juin 2008 13:07 À : math-fun; seqfan@ext.jussieu.fr Objet : Add to n its second smallest non-divider. Loop Hello MathFun & SeqFans, Rule: < Add to n its second smallest non-divider. Loop. > Let's start with n = 7, for instance Is 1 a divider of 7? yes 2 no 3 no --> then new n = 7+3 = 10 Is 1 a divider of 10? yes 2 yes 3 no 4 no --> then new n =10+4= 14 Is 1 a divider of 14? yes 2 yes 3 no 4 no --> then new n =14+4= 18 Is 1 a divider of 18? yes 2 yes 3 yes 4 no 5 no --> then new n =18+5= 23 ... etc. Sequence starting with 7 is: 7,10,14,18,23,... Sequence starting with 1 is: 1,4,9,13,16,21,... [not in the OEIS] Sequence starting with 2 is: 2,6,11,14,18,23,... [merges with "7-seq"] Sequence starting with 3 is: 3,7,10,14,... [merges with "7-seq"] Sequence starting with 5 is: 5,8,13,16,... [merges with "1-seq"] etc. We might map those sequences like this: 1--4--9---13--16--21--25--28--32--37--40 ... | | | 5--8---+ 29--+ | | 2--6--11--14--18--23--26--30------+ | | | 3--7--10--+ | 33--+ | 12--19--22--+ | | 15--+ | | 17--20--+ 24--31--34--38--42 ... | | 27--+ 35--+ What number starts the longest sequence containing 2008? Best, E. --- P.-S. This rule is not very productive: < Add to n its first smallest non-divider. Loop. > What about: < Add to n its third smallest non-divider. Loop. > Etc.
From: "Eric Angelini" <Eric.Angelini@kntv.be>
Rule D2:
< Add to n its second smallest non-divider. Loop. >
What number starts the longest sequence containing 2008? 1961,1964,1969,1972,1977,1981,1984,1989,1993,1996,2001,2005,2008 (length 13) Other question : What numbers CANNOT BE PART of a Rule D2 sequence (except for first term) ? 1,2,3,5,12,15,17,24,27,29,35,36,39,41,45,48,51,53,60,63,65,72,75,77,84,87,89,95,96,99,101,105,108,111,113,120,123, 125,132,135,137,144,147,149,155,156,159,161,165,168,171,173,180,183,185,192,195,197,...
What about: Rule D3 < Add to n its third smallest non-divider. Loop. >
Rule D3 Sequences : 1,5,9,14,19,23,27,32,38,43,47,51,56,62,67,71,75,81,86,91,95,99, , 2,7,11,15,21,26,31,35,39,44,50,56,62,67,71,75,81,86,91,95,99, , 3,8,14,19,23,27,32,38,43,47,51,56,62,67,71,75,81,86,91,95,99, , 4,10,16,22,27,32,38,43,47,51,56,62,67,71,75,81,86,91,95,99, , 5,9,14,19,23,27,32,38,43,47,51,... .... What numbers CANNOT BE PART of a Rule D3 sequence (except for first term) ? 1,2,3,12,24,36,48,60,72,84,96,108,120,132,144,156,168,180,192,204,216,228,240,252,264,276,288,300,312,324,336,348, 360,372,384,396,408,420,432,444,456,468,480,492,504,516,528,540,552,564,576,588,600,612,624,636,648,660,672,684,69 6,720,732,744,756,768,780,792,804,816,828,840,852,864,876,888,900,912,924,936,948,960,972,984,996,1008,1020,1032,1 044,1056,1068,1080,1092,1104,1116,1128,1140,1152,1164,1176,1188,1200,1212,1224,1236,1248,1260,1272,1284,1296,1308, 1320,1332,1344,1356,1368,1380,1392,1404,1416,1428,1440,1452,1464,1476,1488,1500,1512,1524,1536,1560,1572,1584,1596 ,1608,1620,1632,1644,1656,1668,1680,1692,1704,1716,1728,1740,1752,1764,1776,1788,1800,1812,1824,1836,1848,1860,187 2,1884,1896,1908,1920,1932,1944,1956,1968,1980,1992,2000,2004,2008 2008 is not reachable - The above numbers are 'nearly' all multiple of 6
Eric Added : What about: Rule DN < Add to n the n-th smallest number not dividing n >
This gives the following sequence : 1,3,8,20,46,96,204,420,864,1752,3520,7068,14160,28360,56736,113508,227040,454176,908424,1816944,3633908,7267828, 14535662,29071328,... regards, JT et amitiés à Eric. ---------------------------------- http://www.echolalie.com/gbnums http://www.echolalie.org/wiki
This rule simply takes n to 2n + tau(n). Franklin T. Adams-Watters -----Original Message----- From: Eric Angelini <Eric.Angelini@kntv.be> Could please someone compute a few terms more of: < Add to n the n-th smallest number not dividing n > (this is a kind of self-generalization of the rule herunder) I've found this first few terms: S = 1,3,8,20,46,96,... Best, É. (not in the OEIS though 1,3,8,20,46 gives 4 hits)
participants (3)
-
Eric Angelini -
franktaw＠netscape.net -
Jacques Tramu