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 A186495 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=5i (A008587) and g(j)=j-th pentagonal number (A000326).  Complement of A186496. 4
 3, 4, 6, 7, 9, 10, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 63, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 100, 102, 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, 135, 136, 138, 139, 140 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 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 after the pentagonal number: a=(3,4,6,7,9,10,12,13,14,15,17,...)=A186495, b=(1,2,5,8,11,16,20,26,32,38,46,..)=A186496. 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}]  (* A186495 *) Table[b[n], {n, 1, 100}]  (* A186496 *) CROSSREFS Cf. A000326, A008587, A186350, A186493, A186494, A186496. Sequence in context: A130269 A290730 A246443 * A184746 A186227 A258048 Adjacent sequences:  A186492 A186493 A186494 * A186496 A186497 A186498 KEYWORD nonn AUTHOR Clark Kimberling, Feb 22 2011 STATUS approved

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Last modified May 20 10:33 EDT 2022. Contains 353871 sequences. (Running on oeis4.)