A056535 Mapping from the ordering by sum to the ordering by product of the ordered pairs. Inverse permutation to A056534.

1, 2, 3, 4, 7, 5, 6, 12, 13, 8, 9, 18, 22, 19, 10, 11, 25, 32, 33, 26, 14, 15, 31, 43, 48, 44, 34, 16, 17, 39, 55, 63, 64, 56, 40, 20, 21, 47, 68, 80, 86, 81, 69, 49, 23, 24, 54, 79, 98, 107, 108, 99, 82, 57, 27, 28, 62, 93, 116, 129, 136, 130, 117, 94, 65, 29, 30, 72, 106

Offset

1,2

Comments

The last term of the each row r of the triangle is the first term of that row + (tau(r)-1).

As an array, T(n,k) is the index of the k-th term of A027750 whose value is n. - Michel Marcus, Oct 15 2015

Links

Table of n, a(n) for n=1..69.

Index entries for sequences that are permutations of the natural numbers

Formula

[seq(nthmember(j, A056534), j=1..105)];

Example

As a triangle, sequence begins:
1;
2, 3;
4, 7, 5;
6, 12, 13, 8;
9, 18, 22, 19, 10;
...
As an array, sequence begins:
1,   2,  4,  6,  9,  11,  15, ...
3,   7, 12, 18, 25,  31,  39, ...
5,  13, 22, 32, 43,  55,  68, ...
8,  19, 33, 48, 63,  80,  98, ...
10, 26, 44, 64, 86, 107, 129, ...
...

Maple

Maple procedure nthmember given in A054426.

Mathematica

a[n_] := If[p = Position[A056534, n]; p != {}, p[[1, 1]], 0]; (* Jean-François Alcover, Aug 20 2013 *)

Crossrefs

A056535[A000217[i]] = A056535[A000217[i-1]+1]+A000005[i]-1, for all i >= 1.

Left edge: A054519, Right edge: A006218.

Sequence in context: A072658 A099864 A292956 * A026237 A308301 A357578

Adjacent sequences: A056532 A056533 A056534 * A056536 A056537 A056538

Keyword

nonn,tabl

Author

Antti Karttunen, Jun 20 2000

Status

approved