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 A186352 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the odd numbers and the triangular numbers. Complement of A186353. 4
 2, 4, 5, 7, 8, 10, 11, 13, 14, 15, 17, 18, 19, 20, 22, 23, 24, 25, 27, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 137, 138, 139, 140, 141 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..120. FORMULA a(n)=n+floor(-1/2+sqrt(4n-3/4))=A186352(n). b(n)=n+floor((n^2+n+1)/4)=A186353(n). EXAMPLE First, write 1..3..5..7..9..11..13..15..17..21..23.. (odds) 1..3....6.....10.......15......21.... (triangular) Then replace each number by its rank, where ties are settled by ranking the odd number after the triangular: a=(2,4,5,7,8,10,11,13,14,15,....)=A186352 b=(1,3,6,9,12,16,21,26,31,37,...)=A186353. 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=2; v=-1; x=1/2; y=1/2; (* odds and triangular *) h[n_]:=(-y+(4x(u*n+v-d)+y^2)^(1/2))/(2x); a[n_]:=n+Floor[h[n]]; (* rank of u*n+v *) k[n_]:=(x*n^2+y*n-v+d)/u; b[n_]:=n+Floor[k[n]]; (* rank of x*n^2+y*n+d *) Table[a[n], {n, 1, 120}] (* A186352 *) Table[b[n], {n, 1, 100}] (* A186353 *) CROSSREFS Cf. A186350, A186351, A186353. Sequence in context: A078934 A026496 A056127 * A186157 A072633 A037087 Adjacent sequences: A186349 A186350 A186351 * A186353 A186354 A186355 KEYWORD nonn AUTHOR Clark Kimberling, Feb 18 2011 STATUS approved

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Last modified November 30 05:42 EST 2023. Contains 367454 sequences. (Running on oeis4.)