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 A186288 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 pentagonal numbers. Complement of A186289. 3
 1, 3, 5, 7, 9, 11, 12, 14, 16, 18, 20, 21, 23, 25, 27, 29, 31, 32, 34, 36, 38, 40, 41, 43, 45, 47, 49, 51, 52, 54, 56, 58, 60, 61, 63, 65, 67, 69, 71, 72, 74, 76, 78, 80, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 100, 101, 103, 105, 107, 109, 110, 112, 114, 116, 118, 120, 121, 123, 125, 127, 129, 130, 132, 134, 136, 138, 140, 141, 143, 145, 147, 149, 150, 152, 154, 156, 158, 160, 161, 163, 165, 167, 169, 170, 172, 174, 176, 178, 179, 181 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A186219 for a discussion of adjusted rank sequences. LINKS EXAMPLE First, write 1..4...9....16....25..36..49..... (squares 1....5...12....22....35......51.. (pentagonal) Replace each number by its rank, where ties are settled by ranking the square number before the pentagonal: a=(1,3,5,7,9,11,12,14,....)=A186288. b=(2,4,6,8,10,13,15,17,...)=A186289. MATHEMATICA (* adjusted joint ranking; general formula *) d=1/2; u=1; v=0; w=0; x=3/2; y=-1/2; 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}] (* A186288 *) Table[b[n], {n, 1, 100}] (* A186289 *) CROSSREFS Cf. A186219, A186289, A186290, A186291, A000290 (squares), A000326 (pentagonal). Sequence in context: A186346 A248633 A137228 * A272915 A094391 A158919 Adjacent sequences: A186285 A186286 A186287 * A186289 A186290 A186291 KEYWORD nonn AUTHOR Clark Kimberling, Feb 17 2011 STATUS approved

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Last modified March 29 08:33 EDT 2023. Contains 361596 sequences. (Running on oeis4.)