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

Author

Charlie Neder, Dec 27 2018

Keywords

• nonn
• easy
• look

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A008619, A004526, A001477, A260617.

Programs

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

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)

Extensions

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