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

1,1

Comments

See A186350 for a discussion of adjusted joint rank sequences.

Links

Table of n, a(n) for n=1..115.

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: A026516 A289012 A358768 * A289072 A287379 A285954

Adjacent sequences: A186490 A186491 A186492 * A186494 A186495 A186496

Keyword

nonn

Author

Clark Kimberling, Feb 22 2011

Status

approved