A347069 - OEIS

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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

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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

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