%I A160217
%S A160217 3,6,7,9,11,14,15,18,19,22,23,25,27,30,31,33,35,38,39,41,43,46,47,50,51,
%T A160217 54,55,57,59,62,63,66,67,70,71,73,75,78,79,82,83,86,87,89,91,94,95,97,
%U A160217 99,102,103,105,107,110,111,114,115,118,119,121,123,126,127,129,131,134
%N A160217 Minimal increasing sequence with a(1)=3 and the property that a(n) and 
               n are both in or both not in A003159.
%C A160217 The primes in this sequence give A160216.
%C A160217 Conjecture: Let m>3 belong to A003159. Define the sequence b(n) to be 
               the minimal increasing sequence with b(1)=m and the property that 
               b(n) and n are both in or both not in A003159. Then a(n)=b(n) for 
               all n larger than some m-dependent minimum index.
%H A160217 V. Shevelev, <a href="http://arXiv.org/abs/0904.2101">Several results 
               on sequences which are similar to the positive integers</a>, arXiv:0904.2101 
               [math.NT]
%F A160217 a(n+1)=min{ m>a(n): A035263(m)=A035263(n+1) }.
%F A160217 a(n)=2n+1, if A007814(n) is even. a(n)=2n+2, if A007814(n) is odd.
%F A160217 A010060(a(n))=1-A010060(n)
%F A160217 For n>=1, A010060(a(n))= A010060(A004760(n+1)). See also A160230. [From 
               Vladimir Shevelev (shevelev(AT)bgu.ac.il), May 05 2009]
%e A160217 n=2 is not in A003159. So a(2) is the smallest number larger than a(1)=3 
               which is not in A003159. This excludes 4 and 5 which are in A003159 
               and leads to a(2)=6.
%Y A160217 Cf. A003159, A007814, A010060, A160216, A159619.
%Y A160217 Cf. A004760 A160230 [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), 
               May 05 2009]
%Y A160217 Sequence in context: A026415 A026406 A047558 this_sequence A135412 A082847 
               A047242
%Y A160217 Adjacent sequences: A160214 A160215 A160216 this_sequence A160218 A160219 
               A160220
%K A160217 nonn
%O A160217 1,1
%A A160217 Vladimir Shevelev (shevelev(AT)bgu.ac.il), May 04 2009
%E A160217 Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 08 2009