A186220 Adjusted joint rank sequence of (g(i)) and (f(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the triangular numbers and squares. Complement of A186219.

2, 4, 6, 9, 11, 14, 16, 18, 21, 23, 26, 28, 30, 33, 35, 38, 40, 42, 45, 47, 50, 52, 55, 57, 59, 62, 64, 67, 69, 71, 74, 76, 79, 81, 84, 86, 88, 91, 93, 96, 98, 100, 103, 105, 108, 110, 112, 115, 117, 120, 122, 125, 127, 129, 132, 134, 137, 139, 141, 144, 146, 149, 151, 154, 156, 158, 161, 163, 166, 168, 170, 173, 175, 178, 180, 182, 185, 187, 190, 192, 195, 197, 199, 202, 204, 207, 209, 211, 214, 216, 219, 221, 224, 226, 228, 231, 233, 236, 238, 240

Offset

1,1

Comments

See A186219.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

See A186219.

Example

First, write
1..3...6..10..15...21..28..36..45...  (triangular)
1....4.. 9......16...25....36....49.. (square)
Replace each number by its rank, where ties are settled by ranking the triangular number before the square:
a=(1,3,5,7,8,10,12,13,...) = A186219;
b=(2,4,6,9,11,14,16,18,...) = A186220.

Mathematica

(See A186219.)
Table[n + Floor[(-1 + Sqrt[8*n^2 + 3])/2], {n, 1, 100}] (* G. C. Greubel, Aug 26 2018 *)

Prog

(PARI) vector(100, n, n + floor((-1 + sqrt(8*n^2 + 3))/2)) \\ G. C. Greubel, Aug 26 2018
(Magma) [n + Floor((-1 + Sqrt(8*n^2 + 3))/2): n in [1..100]]; // G. C. Greubel, Aug 26 2018

Crossrefs

Cf. A186219, A186221, A186222.

Sequence in context: A203988 A160813 A247515 * A285075 A186316 A265286

Adjacent sequences: A186217 A186218 A186219 * A186221 A186222 A186223

Keyword

nonn

Author

Clark Kimberling, Feb 15 2011

Status

approved