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.

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

Offset: 1

Author

Clark Kimberling, Feb 22 2011

Keywords

• nonn

Comments

See A186350 for a discussion of adjusted joint rank sequences.

Examples

			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.
		

Crossrefs

Cf. A186350, A186494, A186495, A186496.

Programs

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 *)