

A186324


Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the squares and octagonal numbers. Complement of A186325.


4



1, 3, 5, 6, 8, 9, 11, 12, 14, 16, 17, 19, 20, 22, 23, 25, 27, 28, 30, 31, 33, 35, 36, 38, 39, 41, 42, 44, 46, 47, 49, 50, 52, 53, 55, 57, 58, 60, 61, 63, 65, 66, 68, 69, 71, 72, 74, 76, 77, 79, 80, 82, 83, 85, 87, 88, 90, 91, 93, 94, 96, 98, 99, 101, 102, 104, 106, 107, 109, 110, 112, 113, 115, 117, 118, 120, 121, 123, 124, 126, 128, 129, 131, 132, 134, 135, 137, 139, 140, 142, 143, 145, 147, 148, 150, 151, 153, 154, 156, 158
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OFFSET

1,2


COMMENTS

See A186219 for a discussion of adjusted joint rank sequences.


LINKS



EXAMPLE

First, write
1..4...9..16....25..36....49..64... (squares)
1....8.......21........40........65. (octagonal)
Replace each number by its rank, where ties are settled by ranking the square number before the octagonal:
a=(1,3,5,6,8,9,11,12,14,...)=A186324
b=(2,4,7,10,13,15,18,21,...)=A186325.


MATHEMATICA

(* adjusted joint ranking; general formula *)
d=1/2; u=1; v=0; w=0; x=3; y=2; z=0;
h[n_]:=y+(4x(u*n^2+v*n+wzd)+y^2)^(1/2);
a[n_]:=n+Floor[h[n]/(2x)];
k[n_]:=v+(4u(x*n^2+y*n+zw+d)+v^2)^(1/2);
b[n_]:=n+Floor[k[n]/(2u)];
Table[a[n], {n, 1, 100}] (* A186324 *)
Table[b[n], {n, 1, 100}] (* A186325 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



