A349192 Irregular triangle T(m,k) = inverse permutation of S(m,k) = A349191 read as an irregular triangle.

1, 2, 1, 4, 2, 1, 3, 6, 2, 1, 4, 3, 5, 8, 2, 1, 6, 4, 7, 3, 5, 11, 3, 2, 8, 5, 10, 4, 6, 1, 7, 9, 15, 3, 2, 11, 6, 13, 5, 7, 1, 9, 12, 4, 8, 10, 14, 18, 3, 2, 14, 7, 16, 6, 8, 1, 10, 15, 4, 9, 12, 17, 5, 11, 13, 24, 4, 3, 19, 10, 21, 9, 11, 2, 14, 20, 6, 12, 16

Offset: 1

Author

Michael De Vlieger, Nov 09 2021

Keywords

• nonn
• tabf

Comments

We find k at S(m,k) where S is A349191 read as an irregular triangle. Alternatively, we find prime(k) at U(m,k) where U is A348907 read as an irregular triangle.

Examples

			First rows of T(m,k):
  m\k   1   2   3   4   5   6   7   8   9  10  11
  -----------------------------------------------
  1:    1
  2:    2   1
  3:    4   2   1   3
  4:    6   2   1   4   3   5
  5:    8   2   1   6   4   7   3   5
  6:   11   3   2   8   5  10   4   6   1   7   9
  ...
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10237 (rows 1 <= n <= 35, flattened)
• Michael De Vlieger, Log-log scatterplot of T(m,k) 1 <= m <= 36.

Crossrefs

Cf. A000027, A000040, A000720, A338237, A348907, A349191.

Programs

Mathematica

c = 0; Flatten@ Map[Table[If[k == 1, Length[#] + 1, FirstPosition[#, k - 1][[1]]], {k, If[IntegerQ@ #, # + 1, 1] &@ Max[#]}] &, {{}}~Join~Most@ SplitBy[Reap[Do[Set[a[i], If[PrimeQ[i], i; c++, a[i - c]]]; Sow[a[i]], {i, 2, 100}]][[-1, -1]], # == 0 &][[2 ;; -1 ;; 2]]]

Formula

Row lengths are in A338237.