%I A111698 
%S A111698 1,5,9,2,7,12,3,10,15,4,13,18,6,16,21,8,19,24,11,22,27,14,25,30,17,28,
%T A111698 33,20,31,36,23,34,39,26,37,42,29,40,45,32,43,48,35,46,51,38,49,54,41,
%U A111698 52,57,44,55,60,47,58,63,50,61,66,53,64,69,56,67,72,59,70,75,62,73,78
%N A111698 a(1)=1. Skipping over integers occurring earlier in the sequence, count down a composite 
               from a(n) to get a(n+1) so that a(n+1) is the smallest possible positive 
               integer arrived at this way. If there are no positive integers at 
               a distance of a composite number of yet unused integers, instead 
               count up from a(n) 4 (the lowest composite positive integer) positions 
               (skipping already occurring integers) to get a(n+1).
%e A111698 The first 5 terms of the sequence can be plotted on the number line as:
%e A111698 1,2,*,*,5,*,7,*,9,*,*,*.
%e A111698 Now a(5) is 7. Counting down from 7 gets a noncomposite (1,2, or 3) number of steps 
               to arrive at each yet unused positive integer. So we instead count 
               up 4 positions - skipping the 9 as we count - to arrive at 12 (which 
               is at the right-most * of the number-line above).
%e A111698 After the 14th term, the successive differences between terms take on the pattern
		5,-13,11,5,-13,11,...
%H A111698 Diana Mecum, <a href="http://www.research.att.com/~njas/sequences/b111698.txt">Table 
               of n, a(n) for n = 1..1011</a>                
%Y A111698 Cf. A111453, A111118.
%Y A111698 Sequence in context: A021632 A011494 A030125 this_sequence A021948 A111453 A129956
%Y A111698 Adjacent sequences: A111695 A111696 A111697 this_sequence A111699 A111700 A111701
%K A111698 nonn
%O A111698 1,2
%A A111698 Leroy Quet (qq-quet(AT)mindspring.com), Nov 17 2005
%E A111698 More terms from Diana Mecum (diana.mecum(AT)gmail.com), August 3 2008