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.

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

Offset

1,1

Links

Table of n, a(n) for n=1..120.

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: A290730 A369856 A246443 * A184746 A186227 A258048

Adjacent sequences: A186492 A186493 A186494 * A186496 A186497 A186498

Keyword

nonn

Author

Clark Kimberling, Feb 22 2011

Status

approved