login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A190618
Self describing sequence related to Markov numbers.
1
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
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
Sequence in context: A283750 A156679 A344813 * A309585 A004627 A066782
KEYWORD
nonn
AUTHOR
Wouter Meeussen, May 14 2011
STATUS
approved