Riffs & Rotes

[Jon Awbrey]

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R&R.  Note 13

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A108371 [pending]

Table of primal compositional powers (n o)^k, where "o" denotes the
primal composition operator, as illustrated in sequence A106177,
and where (n o)^k = n o ... o n, with k occurrences of n.

First 120:

  1, 2, 1, 3, 2, 1, 4, 1, 2, 1, 5, 1, 1, 2, 1, 6, 1, 1, 1, 2,
  1, 7, 6, 1, 1, 1, 2, 1, 8, 1, 6, 1, 1, 1, 2, 1, 9, 1, 1, 6,
  1, 1, 1, 2, 1,10, 9, 1, 1, 6, 1, 1, 1, 2, 1,11,10, 9, 1, 1,
  6, 1, 1, 1, 2, 1,12, 1,10, 9, 1, 1, 6, 1, 1, 1, 2, 1,13,18,
  1,10, 9, 1, 1, 6, 1, 1, 1, 2, 1,14, 1,12, 1,10, 9, 1, 1, 6,
  1, 1, 1, 2, 1,15,14, 1,18, 1,10, 9, 1, 1, 6, 1, 1, 1, 2, 1

Triangular Array:

  1
  2  1
  3  2  1
  4  1  2  1
  5  1  1  2  1
  6  1  1  1  2  1
  7  6  1  1  1  2  1
  8  1  6  1  1  1  2  1
  9  1  1  6  1  1  1  2  1
 10  9  1  1  6  1  1  1  2  1
 11 10  9  1  1  6  1  1  1  2  1
 12  1 10  9  1  1  6  1  1  1  2  1
 13 18  1 10  9  1  1  6  1  1  1  2  1
 14  1 12  1 10  9  1  1  6  1  1  1  2  1
 15 14  1 18  1 10  9  1  1  6  1  1  1  2  1

Table:  T(n,k) = (n o)^k

` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `T(n,k)
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `\ /
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 1 . 1
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `\ / \ /
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 2 . 1 . 2
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `\ / \ / \ /
` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 3 . 2 . 1 . 3
` ` ` ` ` ` ` ` ` ` ` ` ` ` `\ / \ / \ / \ /
` ` ` ` ` ` ` ` ` ` ` ` ` ` 4 . 3 . 2 . 1 . 4
` ` ` ` ` ` ` ` ` ` ` ` ` `\ / \ / \ / \ / \ /
` ` ` ` ` ` ` ` ` ` ` ` ` 5 . 4 . 1 . 2 . 1 . 5
` ` ` ` ` ` ` ` ` ` ` ` `\ / \ / \ / \ / \ / \ /
` ` ` ` ` ` ` ` ` ` ` ` 6 . 5 . 1 . 1 . 2 . 1 . 6
` ` ` ` ` ` ` ` ` ` ` `\ / \ / \ / \ / \ / \ / \ /
` ` ` ` ` ` ` ` ` ` ` 7 . 6 . 1 . 1 . 1 . 2 . 1 . 7
` ` ` ` ` ` ` ` ` ` `\ / \ / \ / \ / \ / \ / \ / \ /
` ` ` ` ` ` ` ` ` ` 8 . 7 . 6 . 1 . 1 . 1 . 2 . 1 . 8
` ` ` ` ` ` ` ` ` `\ / \ / \ / \ / \ / \ / \ / \ / \ /
` ` ` ` ` ` ` ` ` 9 . 8 . 1 . 6 . 1 . 1 . 1 . 2 . 1 . 9
` ` ` ` ` ` ` ` `\ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
` ` ` ` ` ` ` `10 . 9 . 1 . 1 . 6 . 1 . 1 . 1 . 2 . 1 . 10
` ` ` ` ` ` ` `\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
` ` ` ` ` ` `11 . 10. 9 . 1 . 1 . 6 . 1 . 1 . 1 . 2 . 1 . 11
` ` ` ` ` ` `\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
` ` ` ` ` `12 . 11. 10. 9 . 1 . 1 . 6 . 1 . 1 . 1 . 2 . 1 . 12
` ` ` ` ` `\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
` ` ` ` `13 . 12. 1 . 10. 9 . 1 . 1 . 6 . 1 . 1 . 1 . 2 . 1 . 13
` ` ` ` `\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
` ` ` `14 . 13. 18. 1 . 10. 9 . 1 . 1 . 6 . 1 . 1 . 1 . 2 . 1 . 14
` ` ` `\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
` ` `15 . 14. 1 . 12. 1 . 10. 9 . 1 . 1 . 6 . 1 . 1 . 1 . 2 . 1 . 15
` ` `\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
` `16 . 15. 14. 1 . 18. 1 . 10. 9 . 1 . 1 . 6 . 1 . 1 . 1 . 2 . 1 . 16

| N.J.A. Sloane,
|'On-Line Encyclopedia of Integer Sequences',
| In: http://www.research.att.com/~njas/sequences/
| Cf. http://www.research.att.com/projects/OEIS?Anum=A061396
| Cf. http://www.research.att.com/projects/OEIS?Anum=A062537
| Cf. http://www.research.att.com/projects/OEIS?Anum=A106177
| Cf. http://www.research.att.com/projects/OEIS?Anum=A106178
| Cf. http://www.research.att.com/projects/OEIS?Anum=A108352
| Cf. http://www.research.att.com/projects/OEIS?Anum=A108370
| Cf. http://www.research.att.com/projects/OEIS?Anum=A108372
| Cf. http://www.research.att.com/projects/OEIS?Anum=A108373

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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