Sequence A028931 in OEIS (see: https://oeis.org/A028931)
Strings giving winning positions in Tchoukaillon (or Mancala) solitaire

Using the chromatic (tet-12) scale, (if C=0, 12, 24…) the integers in this sequence correspond exactly to six consecutive semi-tones from G# to C#, evenly bisecting the octave & omitting the other half of the scale from D to F# (see keyboard image & table below). The recursive pattern is C, C#, G#, A, Bb, B…the only possible collection of 6 pitches that avoids a tritone (IC6).

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

0 1 20 21 310 311 4200 4201 4220 4221 53110 53111 642000 642001 642020 642021 642310 642311 7531200 7531201 7531220 7531221 86420110 86420111 86424000 86424001 86424020 86424021 86424310 86424311

C C# G# A Bb B C C# G# A Bb B C C# G# A Bb B C C# G# A Bb B C C# G# A Bb B