<div dir="ltr">Sequence Fan Group,<br><br>I discovered an intriguing fact about sequence A111698 submitted by Leroy Quet in the process of adding sequence terms.<br><br>If there are four or more non-listed integers less than a(n) for some arbitrary n, then we choose the smallest one which is a composite distance from a(n), (distance here defined in steps of non-listed integers). This smallest integer is chosen for a(n+1).<br>
<br>However, if there are three or fewer non-listed integers less than a(n), then the fourth non-listed integer greater than a(n) is chosen for a(n+1).<br><br>I have found two patterns for this sequence. The first is that there is a pattern 0,3,6,0,3,6,0,3,6,... which states the lengths of the "LessThanList" for each term. In other words, a(6) = 12. There are six integers less than 12 which are not already listed in the sequence at this point, {3,4,6,8,10,11}. a(7) = 3. There are no integers not already on the list which are less than 3 at this point. a(8) = 10. There are three integers less than 10 which are not already on the list at this point, {4,6,8}.<br>
<br>I have worked this out to 1200 terms and see this pattern consistently.<br><br>Also, after the 14th term, the sequence becomes regular in the following way. The difference between successive terms is as follows: 5,-13,11,5,-13,11,...<br>
<br>This sequence starts out looking random but becomes regular.<br><br>Please see attached files.<br><br>Diana M.<br clear="all"><br>-- <br>Diana Does It! ~~> <a href="http://www.DianaDoesIt.com">www.DianaDoesIt.com</a><br>
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