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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.

%I A186220 #8 Sep 08 2022 08:45:55
%S A186220 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 A186220 59,62,64,67,69,71,74,76,79,81,84,86,88,91,93,96,98,100,103,105,108,
%U A186220 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 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.
%C A186220 See A186219.
%H A186220 G. C. Greubel, <a href="/A186220/b186220.txt">Table of n, a(n) for n = 1..10000</a>
%F A186220 See A186219.
%e A186220 First, write
%e A186220 1..3...6..10..15...21..28..36..45...  (triangular)
%e A186220 1....4.. 9......16...25....36....49.. (square)
%e A186220 Replace each number by its rank, where ties are settled by ranking the triangular number before the square:
%e A186220 a=(1,3,5,7,8,10,12,13,...) = A186219;
%e A186220 b=(2,4,6,9,11,14,16,18,...) = A186220.
%t A186220 (See A186219.)
%t A186220 Table[n + Floor[(-1 + Sqrt[8*n^2 + 3])/2], {n, 1, 100}] (* _G. C. Greubel_, Aug 26 2018 *)
%o A186220 (PARI) vector(100, n, n + floor((-1 + sqrt(8*n^2 + 3))/2)) \\ _G. C. Greubel_, Aug 26 2018
%o A186220 (Magma) [n + Floor((-1 + Sqrt(8*n^2 + 3))/2): n in [1..100]]; // _G. C. Greubel_, Aug 26 2018
%Y A186220 Cf. A186219, A186221, A186222.
%K A186220 nonn
%O A186220 1,1
%A A186220 _Clark Kimberling_, Feb 15 2011