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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 Table of n, a(n) for n=1..100. 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 September 23 15:35 EDT 2023. Contains 365554 sequences. (Running on oeis4.)