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 A186328 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 pentagonal numbers and the hexagonal numbers.  Complement of A186329. 4
 1, 3, 5, 7, 9, 11, 13, 15, 16, 18, 20, 22, 24, 26, 28, 29, 31, 33, 35, 37, 39, 41, 43, 44, 46, 48, 50, 52, 54, 56, 57, 59, 61, 63, 65, 67, 69, 71, 72, 74, 76, 78, 80, 82, 84, 85, 87, 89, 91, 93, 95, 97, 99, 100, 102, 104, 106, 108, 110, 112, 113, 115, 117, 119, 121, 123, 125, 126, 128, 130, 132, 134, 136, 138, 140, 141, 143, 145, 147, 149, 151, 153, 154, 156, 158, 160, 162, 164, 166, 168, 169, 171, 173, 175, 177, 179, 181, 182, 184, 186 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A186219 for a discussion of adjusted joint rank sequences. LINKS EXAMPLE First, write 1..5...12....22.....35......  (pentagonal) 1....6....15....28.......45.. (hexagonal) Then replace each number by its rank, where ties are settled by ranking the pentagonal number before the hexagonal: a=(1,3,5,7,9,11,13,15,16,....)=A186328 b=(2,4,6,8,10,12,14,17,19,...)=A186329. MATHEMATICA (* adjusted joint ranking; general formula *) d=1/2; u=3/2; v=-1/2; w=0; x=2; y=-1; 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}]  (* A186328 *) Table[b[n], {n, 1, 100}]  (* A186329 *) CROSSREFS Cf. A186219, A186329, A186330, A186331, A000384 (pentagonal), A000384 (hexagonal). Sequence in context: A120890 A321499 A134322 * A063460 A247429 A187232 Adjacent sequences:  A186325 A186326 A186327 * A186329 A186330 A186331 KEYWORD nonn AUTHOR Clark Kimberling, Feb 17 2011 STATUS approved

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Last modified May 26 05:25 EDT 2019. Contains 323579 sequences. (Running on oeis4.)