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 A186497 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=3i-2 and g(j)=j-th triangular number.  Complement of A186498. 2
 1, 4, 6, 7, 9, 11, 12, 14, 15, 16, 18, 19, 21, 22, 23, 25, 26, 27, 28, 30, 31, 32, 34, 35, 36, 37, 39, 40, 41, 42, 43, 45, 46, 47, 48, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 99, 100, 101, 102, 103, 104, 105, 106, 108, 109, 110, 111, 112, 113, 114, 116, 117, 118, 119, 120, 121, 122, 123, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 136, 137, 138, 139, 140, 141, 142, 144, 145, 146 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A186350 for a discussion of adjusted joint rank sequences. LINKS EXAMPLE First, write 1..4..7.10..13..16..19..22..25..28..31. (3i-2), 1.3..6..10....15.......21.......28.....(j(j+1)/2). Then replace each number by its rank, where ties are settled by ranking 3i-2 before j(j+1)/2: a=(1,4,6,7,9,11,12,14,15,16,18,...)=A186497, b=(2,3,5,8,10,13,17,20,24,29,33,..)=A186498. MATHEMATICA (* Adjusted joint rank sequences a and b, using general formula for ranking 1st degree u*n+v and 2nd degree x*n^2+y*n+z. *) d=1/2; u=3; v=-2; x=1/2; y=1/2; h[n_]:=(-y+(4x(u*n+v-d)+y^2)^(1/2))/(2x); a[n_]:=n+Floor[h[n]]; k[n_]:=(x*n^2+y*n-v+d)/u; b[n_]:=n+Floor[k[n]]; Table[a[n], {n, 1, 120}]  (* A186497 *) Table[b[n], {n, 1, 100}]  (* A186498 *) CROSSREFS Cf. A186350, A186498, A186499, A186500. Sequence in context: A101993 A002481 A183870 * A193627 A256792 A085817 Adjacent sequences:  A186494 A186495 A186496 * A186498 A186499 A186500 KEYWORD nonn AUTHOR Clark Kimberling, Feb 22 2011 STATUS approved

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Last modified December 12 22:06 EST 2019. Contains 329963 sequences. (Running on oeis4.)