

A186320


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 heptagonal numbers. Complement of A186321.


4



1, 3, 5, 6, 8, 10, 11, 13, 14, 16, 18, 19, 21, 23, 24, 26, 28, 29, 31, 32, 34, 36, 37, 39, 41, 42, 44, 46, 47, 49, 50, 52, 54, 55, 57, 59, 60, 62, 63, 65, 67, 68, 70, 72, 73, 75, 77, 78, 80, 81, 83, 85, 86, 88, 90, 91, 93, 94, 96, 98, 99, 101, 103, 104, 106, 108, 109, 111, 112, 114, 116, 117, 119, 121, 122, 124, 125, 127, 129, 130, 132, 134, 135, 137, 139, 140, 142, 143, 145, 147, 148, 150, 152, 153, 155, 157, 158, 160, 161, 163
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OFFSET

1,2


LINKS



EXAMPLE

First, write
1..4...9..16....25...36...49...64.. (squares)
1....7.......18....34........55.... (heptagonal)
Replace each number by its rank, where ties are settled by ranking the square number before the heptagonal:
b=(2,4,7,9,12,15,17,20,...)=A186321.


MATHEMATICA

(* adjusted joint ranking; general formula *)
d=1/2; u=1; v=0; w=0; x=5/2; y=3/2; 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}] (* A186320 *)
Table[b[n], {n, 1, 100}] (* A186321 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



