A347069 Rectangular array (T(n,k)), by downward antidiagonals: T(n,k) = position of k in the ordering of {h*e^m, h >= 1, 0 <= m <= n}.

1, 2, 1, 4, 2, 1, 5, 4, 2, 1, 6, 5, 4, 2, 1, 8, 6, 5, 4, 2, 1, 9, 8, 6, 5, 4, 2, 1, 10, 9, 8, 6, 5, 4, 2, 1, 12, 11, 9, 8, 6, 5, 4, 2, 1, 13, 13, 11, 9, 8, 6, 5, 4, 2, 1, 15, 14, 13, 11, 9, 8, 6, 5, 4, 2, 1, 16, 16, 14, 13, 11, 9, 8, 6, 5, 4, 2, 1, 17, 17

Offset

1,2

Comments

No two rows are identical.

Links

Table of n, a(n) for n=1..80.

Example

m = 0 gives 1, 2, 3, 4, 5, 6, ...
m = 1 gives e, 2e, 3e, 4e, 5e, ...
Row 1 of the array tells the positions of the positive integers when the numbers for m=0 and m=1 are jointly ranked.  Using decimal approximations, the numbers, jointly ranked, are 1, 2, 2.718, 3, 4, 5, 6.436, 6, 7, 8, 8.154, 9, 10, 10.873, 11, ...
Corner:
  1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 15, 16, 17
  1, 2, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 18
  1, 2, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 18
  1, 2, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 18
  1, 2, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 18
  1, 2, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 18
  1, 2, 4, 5, 6, 8, 9, 11, 13, 14, 16, 17, 18

Mathematica

z = 100; r = N[E];
s[m_] := Range[z] r^m; t[0] = s[0];
t[n_] := Sort[Union[s[n], t[n - 1]]]
row[n_] := Flatten[Table[Position[t[n], N[k]], {k, 1, z}]]
TableForm[Table[row[n], {n, 1, 10}]] (* A347069, array *)
w[n_, k_] := row[n][[k]];
Table[w[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A347069, sequence *)

Crossrefs

Cf. A347065, A347066, A347067, A347068.

Sequence in context: A135152 A329504 A147542 * A365901 A325309 A211956

Adjacent sequences: A347066 A347067 A347068 * A347070 A347071 A347072

Keyword

nonn,tabl

Author

Clark Kimberling, Sep 02 2021

Status

approved