A322832 Values x + y, where the ordered pairs (x,y) are sorted first by maximal coordinate and then lexicographically.

0, 1, 1, 2, 2, 3, 2, 3, 4, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 4, 5, 6, 7, 8, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 6, 7, 8, 9, 10, 11, 12, 7, 8, 9, 10, 11, 12, 13, 7, 8, 9, 10, 11, 12, 13, 14, 8, 9, 10, 11, 12, 13, 14, 15, 8, 9, 10, 11, 12, 13, 14, 15, 16

Offset

0,4

Comments

This sequence consists of runs of length A008619(k) with initial elements A004526(k+1) and final elements A001477(k).

Links

David A. Corneth, Table of n, a(n) for n = 0..10200

Formula

From David A. Corneth, Jan 11 2019: (Start)

a(n^2 + j) = n + j for 0 <= j <= n-1.

a(n^2 + j) = j, n <= j <= 2*n (End)

Example

The sorted pairs (x,y) and their sums x+y are:
(0,0) => 0
(0,1) => 1
(1,0) => 1
(1,1) => 2
(0,2) => 2
(1,2) => 3
(2,0) => 2
(2,1) => 3
(2,2) => 4
(0,3) => 3
etc.

Prog

(PARI) first(n) = {n = (sqrtint(n) + 1) ^ 2; res = vector(n); for(i = 0, sqrtint(n) - 1, res[i^2 + 1] = i; for(j = 1, i - 1, res[i ^ 2 + j + 1] = i + j; ); for(j = i, 2 * i, res[i ^ 2 + j + 1] = j; ) ); res } \\ David A. Corneth, Jan 11 2019

Crossrefs

Cf. A008619, A004526, A001477, A260617.

Sequence in context: A115726 A086413 A069352 * A348389 A073453 A123229

Adjacent sequences: A322829 A322830 A322831 * A322833 A322834 A322835

Keyword

nonn,easy,look

Author

Charlie Neder, Dec 27 2018

Extensions

Edited by N. J. A. Sloane, Dec 28 2018

Status

approved