A186227 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 triangular numbers and heptagonal numbers. Complement of A186228.
1, 3, 4, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 43, 45, 46, 48, 49, 51, 52, 54, 55, 56, 58, 59, 61, 62, 64, 65, 67, 68, 69, 71, 72, 74, 75, 77, 78, 80, 81, 83, 84, 85, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 106, 107, 109, 110, 111, 113, 114, 116, 117, 119, 120, 122, 123, 124, 126, 127, 129, 130, 132, 133, 135, 136, 138, 139, 140, 142, 143, 145
Offset: 1
Keywords
Examples
First, write 1..3..6..10..15..21..28..36..45... (triangular) 1.......7......18......34.......55... (heptagonal) Then replace each number by its rank, where ties are settled by ranking the triangular number before the heptagonal: a=(1,3,4,6,7,9,10,12,...), A186227. b=(2,5,8,11,15,18,21,...), A186228.
Crossrefs
Programs
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Mathematica
(* adjusted joint ranking; general formula *) d=1/2; u=1/2; v=1/2; w=0; x=5/2; y=-3/2; z=0; h[n_]:=-y+(4x(u*n^2+v*n+w-z-d)+y^2)^(1/2); a[n_]:=n+Floor[h[n]/(2x)]; k[n_]:=-v+(4u(x*n^2+y*n+z-w+d)+v^2)^(1/2); b[n_]:=n+Floor[k[n]/(2u)]; Table[a[n],{n,1,100}] (* A186227 *) Table[b[n],{n,1,100}] (* A186228 *)
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