OFFSET
1,1
COMMENTS
Look at the lengths of runs of successive terms that increase by 1.
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.
LINKS
Wouter Meeussen, Table of n, a(n) for n = 1..1186
EXAMPLE
{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
MATHEMATICA
f[x_, y_]:={x, 1/2*(3*x*y + Sqrt[-4*x^2 - 4*y^2 + 9*x^2*y^2]), y};
g[w_List]:=Flatten[{1, Rest/@ Apply[f, Partition[w, 2, 1], {1}] } ];
it=NestList[g, {1, 2}, 12]; novel=(Last/@ Partition[#, 2])&/@ Rest[it];
noveven=Flatten[ Position[Flatten@ novel, _?EvenQ] ];
Flatten[Position[ -1+Length/@Split[noveven, #1+1==#2&] , 3] ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wouter Meeussen, May 14 2011
STATUS
approved