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A078649 Numbers n such that A000002(n)=A000002(n+1) where A000002 is the Kolakoski sequence.

%I A078649 #26 Mar 13 2015 15:43:38
%S A078649 2,4,8,11,13,16,18,22,26,28,31,35,38,40,44,48,51,53,56,58,62,65,67,70,
%T A078649 74,78,80,83,85,89,92,94,97,99,103,107,110,112,115,119,121,124,126,
%U A078649 130,133,135,138,140,144,148,150,153,157,160,162,165,167,171,175,178,180
%N A078649 Numbers n such that A000002(n)=A000002(n+1) where A000002 is the Kolakoski sequence.
%C A078649 Complement sequence of A054353. - _Benoit Cloitre_, Feb 07 2009
%C A078649 This sequence is the union of A074262 and A074263. - _Nathaniel Johnston_, May 02 2011
%C A078649 A054354(a(n)-1) = 0. - _Reinhard Zumkeller_, Aug 03 2013
%C A078649 This is a subsequence of A216345. In particular, this consists of A216345(i) such that A000002(i) = A216345(i+1)-A216345(i) = 2. A013948 is the sequence of all such i. - _Danny Rorabaugh_, Mar 13 2015
%H A078649 Nathaniel Johnston, <a href="/A078649/b078649.txt">Table of n, a(n) for n = 1..10000</a>
%F A078649 a(n) is probably asymptotic to 3*n.
%F A078649 a(n) = A216345(A013948(n)). - _Danny Rorabaugh_, Mar 13 2015
%p A078649 isA078649 := proc(n)
%p A078649     if A000002(n) = A000002(n+1) then
%p A078649         true;
%p A078649     else
%p A078649         false;
%p A078649     end if;
%p A078649 end proc:
%p A078649 A078649 := proc(n)
%p A078649     option remember;
%p A078649     if n = 1 then
%p A078649         2;
%p A078649     else
%p A078649         for a from procname(n-1)+1 do
%p A078649             if isA078649(a) then
%p A078649                 return a;
%p A078649             end if;
%p A078649         end do:
%p A078649     end if;
%p A078649 end proc:
%p A078649 seq(A078649(n),n=1..50) ; # _R. J. Mathar_, Nov 15 2014
%t A078649 a2 = {1, 2, 2}; Do[ a2 = Join[a2, {1+Mod[n-1, 2]}], {n, 3, 80}, {a2[[n]]}]; a3 = Accumulate[a2]; Complement[ Range[ Last[a3]], a3] (* _Jean-François Alcover_, Jun 18 2013 *)
%o A078649 (Haskell)
%o A078649 a078649 n = a078649_list !! (n-1)
%o A078649 a078649_list = map (+ 1) $ filter ((== 0) . a054354) [1..]
%o A078649 -- _Reinhard Zumkeller_, Aug 03 2013
%Y A078649 Cf. A054353, A074262, A074263, A013948, A216345.
%K A078649 nonn,easy
%O A078649 1,1
%A A078649 _Benoit Cloitre_, Dec 14 2002