cp's OEIS Frontend

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.

%I A186493 #10 Apr 09 2015 14:58:11
%S A186493 2,4,6,7,9,10,11,13,14,15,17,18,19,20,22,23,24,25,27,28,29,30,31,33,
%T A186493 34,35,36,37,38,40,41,42,43,44,45,47,48,49,50,51,52,53,55,56,57,58,59,
%U A186493 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
%N 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.
%C A186493 See A186350 for a discussion of adjusted joint rank sequences.
%e A186493 First, write
%e A186493 ....5..10..15..20..25..30..35..40.. (5i),
%e A186493 1..5......12......22............35..(pentagonal numbers).
%e A186493 Then replace each number by its rank, where ties are settled by ranking 5i before the pentagonal number:
%e A186493 a=(2,4,6,7,9,10,11,13,14,15,17,...)=A186493,
%e A186493 b=(1,3,5,8,12,16,21,26,32,39,46,..)=A186494.
%t A186493 (* 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. *)
%t A186493 d=1/2; u=5; v=0; x=3/2; y=-1/2;
%t A186493 h[n_]:=(-y+(4x(u*n+v-d)+y^2)^(1/2))/(2x);
%t A186493 a[n_]:=n+Floor[h[n]];
%t A186493 k[n_]:=(x*n^2+y*n-v+d)/u;
%t A186493 b[n_]:=n+Floor[k[n]];
%t A186493 Table[a[n],{n,1,120}]  (* A186493 *)
%t A186493 Table[b[n],{n,1,100}]  (* A186494 *)
%Y A186493 Cf. A186350, A186494, A186495, A186496.
%K A186493 nonn
%O A186493 1,1
%A A186493 _Clark Kimberling_, Feb 22 2011