A107640 Irregular triangle read by rows: positions of 2's in the triangle generated by the morphism 1->2, 2->3, 3->123 starting from 2.

1, 2, 1, 4, 3, 5, 2, 4, 1, 4, 3, 5, 8, 2, 4, 7, 1, 4, 8, 10, 3, 5, 8, 11, 2, 4, 7, 11, 1, 4, 8, 10, 13, 3, 5, 8, 11, 13, 2, 4, 7, 11, 13, 1, 4, 8, 10, 13, 16, 3, 5, 8, 11, 13, 16, 2, 4, 7, 11, 13, 16, 18, 1, 4, 8, 10, 13, 16, 18, 3, 5, 8, 11, 13, 16, 20

Offset

1,2

Links

Table of n, a(n) for n=1..76.

Example

Begins:
  row triangle    positions of 2's
   1  2        -> 1;
   2  3        -> none;
   3  123      -> 2;
   4  2312     -> 1, 4;
   5  31232    -> 3, 5;
   6  123231   -> 2, 4;
   7  2312331  -> 1, 4;
   8  31232312 -> 3, 5, 8;

Mathematica

s[1] = {2}; s[2] = {3}; s[3] = {1, 2, 3};
t[a_] := Flatten[s /@ a];
p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]];
a = Table[Flatten[Table[If[(Length[p[i]]) >= j && (p[i][[j]] == 2), j, {}], {j, 1, i}]], {i, 1, 20}];
MatrixForm[a] //Flatten

Crossrefs

Cf. A107641.

Sequence in context: A144334 A141210 A244373 * A030065 A362939 A328676

Adjacent sequences: A107637 A107638 A107639 * A107641 A107642 A107643

Keyword

nonn,tabf,changed

Author

Roger L. Bagula, Jun 09 2005

Extensions

Edited by Sean A. Irvine, Jun 28 2026

Status

approved