A186220 - OEIS

%I #8 Sep 08 2022 08:45:55

%S 2,4,6,9,11,14,16,18,21,23,26,28,30,33,35,38,40,42,45,47,50,52,55,57,

%T 59,62,64,67,69,71,74,76,79,81,84,86,88,91,93,96,98,100,103,105,108,

%U 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

%N 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.

%C See A186219.

%H G. C. Greubel, <a href="/A186220/b186220.txt">Table of n, a(n) for n = 1..10000</a>

%F See A186219.

%e First, write

%e 1..3...6..10..15...21..28..36..45...  (triangular)

%e 1....4.. 9......16...25....36....49.. (square)

%e Replace each number by its rank, where ties are settled by ranking the triangular number before the square:

%e a=(1,3,5,7,8,10,12,13,...) = A186219;

%e b=(2,4,6,9,11,14,16,18,...) = A186220.

%t (See A186219.)

%t Table[n + Floor[(-1 + Sqrt[8*n^2 + 3])/2], {n, 1, 100}] (* _G. C. Greubel_, Aug 26 2018 *)

%o (PARI) vector(100, n, n + floor((-1 + sqrt(8*n^2 + 3))/2)) \\ _G. C. Greubel_, Aug 26 2018

%o (Magma) [n + Floor((-1 + Sqrt(8*n^2 + 3))/2): n in [1..100]]; // _G. C. Greubel_, Aug 26 2018

%Y Cf. A186219, A186221, A186222.

%K nonn

%O 1,1

%A _Clark Kimberling_, Feb 15 2011