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

1,2

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.

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.

Formula

Row lengths are in A338237.

Example

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
... (End)

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]]]

Crossrefs

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

Sequence in context: A243070 A243060 A286321 * A118235 A346702 A304624

Adjacent sequences: A349189 A349190 A349191 * A349193 A349194 A349195

Keyword

nonn,tabf

Author

Michael De Vlieger, Nov 09 2021

Status

approved