

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.


4



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS



LINKS



FORMULA



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

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



KEYWORD

nonn


AUTHOR



STATUS

approved



