A186290 Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f and g are the squares and pentagonal numbers. Complement of A186291.

2, 3, 5, 7, 9, 11, 12, 14, 16, 18, 20, 21, 23, 25, 27, 29, 31, 32, 34, 36, 38, 40, 41, 43, 45, 47, 49, 51, 52, 54, 56, 58, 60, 61, 63, 65, 67, 69, 71, 72, 74, 76, 78, 80, 81, 83, 85, 87, 89, 90, 92, 94, 96, 98, 100, 101, 103, 105, 107, 109, 110, 112, 114, 116, 118, 120, 121, 123, 125, 127, 129, 130, 132, 134, 136, 138, 140, 141, 143, 145, 147, 149, 150, 152, 154, 156, 158, 160, 161, 163, 165, 167, 169, 170, 172, 174, 176, 178, 180, 181

Offset

1,1

Comments

See A186219 for a discussion of adjusted joint rank sequences.

Links

Table of n, a(n) for n=1..100.

Example

First, write
1..4...9....16....25..36..49..... (squares
1....5...12....22....35......51.. (pentagonal)
Replace each number by its rank, where ties are settled by ranking the square number after the pentagonal:
a=(2,3,5,7,9,11,12,14,....)=A186290.
b=(1,4,6,8,10,13,15,17,...)=A186291.

Mathematica

(* adjusted joint ranking; general formula *)
d=-1/2; u=1; v=0; w=0; x=3/2; y=-1/2; z=0;
h[n_]:=-y+(4x(u*n^2+v*n+w-z-d)+y^2)^(1/2);
a[n_]:=n+Floor[h[n]/(2x)];
k[n_]:=-v+(4u(x*n^2+y*n+z-w+d)+v^2)^(1/2);
b[n_]:=n+Floor[k[n]/(2u)];
Table[a[n], {n, 1, 100}]  (* A186290 *)
Table[b[n], {n, 1, 100}]  (* A186291 *)

Crossrefs

Sequence in context: A087268 A106765 A190785 * A061979 A050748 A348638

Adjacent sequences: A186287 A186288 A186289 * A186291 A186292 A186293

Keyword

nonn

Author

Clark Kimberling, Feb 17 2011

Status

approved