# Add to n its second smallest non-divider. Loop

Hans Havermann pxp at rogers.com
Wed Jun 25 18:02:51 CEST 2008

```From: "Eric Angelini" <Eric.Angelini at 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,...

> < 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

< 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.

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