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 A186493 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f(i)=5i and g(j)=j-th pentagonal number.  Complement of A186494. 4
 2, 4, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 25, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 134 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A186350 for a discussion of adjusted joint rank sequences. LINKS EXAMPLE First, write ....5..10..15..20..25..30..35..40.. (5i), 1..5......12......22............35..(pentagonal numbers). Then replace each number by its rank, where ties are settled by ranking 5i before the pentagonal number: a=(2,4,6,7,9,10,11,13,14,15,17,...)=A186493, b=(1,3,5,8,12,16,21,26,32,39,46,..)=A186494. 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=5; v=0; x=3/2; 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}]  (* A186493 *) Table[b[n], {n, 1, 100}]  (* A186494 *) CROSSREFS Cf. A186350, A186494, A186495, A186496. Sequence in context: A048284 A026516 A289012 * A289072 A287379 A285954 Adjacent sequences:  A186490 A186491 A186492 * A186494 A186495 A186496 KEYWORD nonn AUTHOR Clark Kimberling, Feb 22 2011 STATUS approved

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Last modified December 10 20:38 EST 2019. Contains 329909 sequences. (Running on oeis4.)