A190618 Self describing sequence related to Markov numbers.

5, 13, 25, 29, 34, 35, 36, 41, 52, 60, 65, 76, 81, 88, 93, 94, 95, 100, 111, 123, 128, 147, 152, 167, 172, 183, 188, 195, 200, 201, 202, 207, 218, 222, 227, 228, 229, 234, 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

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

Cf. A002559

Sequence in context: A283750 A156679 A344813 * A309585 A004627 A066782

Adjacent sequences: A190615 A190616 A190617 * A190619 A190620 A190621

Keyword

nonn

Author

Wouter Meeussen, May 14 2011

Status

approved