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%I #9 Mar 30 2012 18:37:45
%S 5,13,25,29,34,35,36,41,52,60,65,76,81,88,93,94,95,100,111,123,128,
%T 147,152,167,172,183,188,195,200,201,202,207,218,222,227,228,229,234,
%U 245,250,261,266,267,268,273,274,275,280,281,282,287,298,303,314,319,320,321,326,337,342,361,366,381,386,397,402,409,414,415,416,421,432
%N Self describing sequence related to Markov numbers.
%C Look at the lengths of runs of successive terms that increase by 1.
%C The run lengths here are 1,1,1,1,3,1,1,..., with 3's in positions 5, 13, 25, 29, ... , which is the sequence itself.
%H Wouter Meeussen, <a href="/A190618/b190618.txt">Table of n, a(n) for n = 1..1186</a>
%e {5}, {13}, {25}, {29}, {34,35,36}, {41}, {52}.. are viewed as sublists of lengths 1, 1, 1, 1, 3, 1, 1.. with the '3' occurring in 5th place, hence the first element is again 5
%t f[x_,y_]:={x, 1/2*(3*x*y + Sqrt[-4*x^2 - 4*y^2 + 9*x^2*y^2]),y};
%t g[w_List]:=Flatten[{1, Rest/@ Apply[f,Partition[w,2,1],{1}] } ];
%t it=NestList[g,{1,2},12];novel=(Last/@ Partition[#,2])&/@ Rest[it];
%t noveven=Flatten[ Position[Flatten@ novel,_?EvenQ] ];
%t Flatten[Position[ -1+Length/@Split[noveven,#1+1==#2&] ,3] ]
%Y Cf. A002559
%K nonn
%O 1,1
%A _Wouter Meeussen_, May 14 2011
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