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 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. 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A186219 for a general discussion of adjusted joint rank sequences. LINKS EXAMPLE 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. 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 *) CROSSREFS Cf. A186219, A186228, A186237, A186238, Cf. A000217 (triangular numbers) Cf. A000566 (heptagonal numbers) Sequence in context: A246443 A186495 A184746 * A258048 A185543 A026322 Adjacent sequences:  A186224 A186225 A186226 * A186228 A186229 A186230 KEYWORD nonn AUTHOR Clark Kimberling, Feb 16 2011 STATUS approved

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Last modified January 18 17:18 EST 2022. Contains 350455 sequences. (Running on oeis4.)