I calculated more values of the R-sequence.

3

9, 10

27, 28, 30

81, 84, 88, 90, 100, 104

243, 252, 264, 270, 272, 280, 300, 304, 312

729, 736, 756, 784, 792, 810, 816, 840, 880, 900, 912, 928, 936, 992, 1000, 1040

next:

2187, 2208, 2268, 2352,2368, 2376,

2430, 2448, 2464, 2520, 2624, 2640,

2700, 2720, 2736, 2752, 2784, 2800,

2808, 2912, 2976, 3000, 3008, 3040, 3120

next:

6561, 6624, 6784, 6804, 7056, 7104, 7128, 7290, 7344, 7360, 7392, \

7552, 7560, 7616, 7744, 7808, 7840, 7872, 7920, 8100, 8160, 8208, \

8256, 8352, 8400, 8424, 8512, 8576, 8736, 8800, 8928, 9000, 9024, \

9088, 9120, 9152, 9280, 9344, 9360

next:

19683, 19840, 19872, 20000, 20224, 20352, 20412, 20608, 20800, 21168, \

21248, 21312, 21384, 21632, 21870, 21952, 22032, 22080, 22176, 22656, \

22680, 22784, 22848, 23232, 23424, 23520, 23616, 23680, 23760, 23936, \

24300, 24480, 24624, 24640, 24768, 24832, 25056, 25200, 25272, 25536, \

25728, 25856, 25984, 26208, 26240, 26368, 26400, 26752, 26784, 27000, \

27072, 27200, 27264, 27360, 27392, 27456, 27520, 27776, 27840, 27904, \

28000, 28032, 28080, 28288, 28928, 29120

Based on this investigation we cannot find a counterexample to the claim that each i-blocker contains only one (and the same time the smallest) odd number, which is of the form 3^k. 3 plays here a significant role.

Lengths of blockers: **1,1,2,3,6,9,16,21,39,66**

The amount of corresponding primes

1,

1+2=3,

1+2+3=6,..

ie. 1,3,6,12,21,38,63,.. defines corresponding primes in the xi (matrix with k-th column containing ordered (ascending) k-almost primes). We also observe that A215005, i.e. a(n) = a(n-2) + a(n-1) + floor(n/2) + 1, contains 6, 12, 21, 37, 62 (62 but not 63!), but this resemblance has not been verified.

R sequence:

Positions of 3^k are: **1,2,4,7,13,22,38,.. We observe that this starts exactly as A101268, i.e. number of compositions of n into pairwise rel. prime parts.**

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