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%I #10 Mar 30 2012 18:35:45
%S 1,2,3,5,6,7,11,12,13,17,18,21,23,24,25,27,28,29,31,32,33,35,36,37,39,
%T 41,43,44,45,47,52,53,59,60,61,67,68,71,73,74,75,77,78,79,81,83,85,86,
%U 87,89,91,93,94,95,97,98,100,101,103,104,105,107,109,111
%N Start with sequence 1,2,3, after this a(n) is smallest number > a(n-1) coprime to sum of previous elements.
%C Starting with sequence 1 and adding increasing numbers coprime to sum of previous elements yields periodic sequence A001651.
%C By starting with 1,2,3, you get this sequence, apparently non-periodic with sporadic periodic runs of varied length.
%C Sequence appears to have density of about 0.6 with respect to the positive integers.
%C Not all primes are in this sequence, 19 being the first missing prime.
%H David W. Wilson, <a href="/A198191/b198191.txt">Table of n, a(n) for n = 1..10000</a>
%e 1,2,3 are in the sequence by fiat.
%e The element smaller than 4 are 1,2,3 with sum 6. 4 is not coprime to 6, so 4 is excluded.
%e The elements smaller than 5 are 1,2,3 with sum 6. 5 is coprime to 6, so 5 is included.
%e The elements smaller than 6 are 1,2,3,5 with sum 11. 6 is coprime to 11, so 6 is included.
%K nonn
%O 1,2
%A _David W. Wilson_, Oct 21 2011
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