A186225 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 triangular numbers and pentagonal numbers. Complement of A186226.

2, 3, 5, 6, 8, 9, 11, 13, 14, 16, 17, 19, 20, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 38, 39, 41, 43, 44, 46, 47, 49, 50, 52, 54, 55, 57, 58, 60, 61, 63, 65, 66, 68, 69, 71, 73, 74, 76, 77, 79, 80, 82, 84, 85, 87, 88, 90, 91, 93, 95, 96, 98, 99, 101, 102, 104, 106, 107, 109, 110, 112, 114, 115, 117, 118, 120, 121, 123, 125, 126, 128, 129, 131, 132, 134, 136, 137, 139, 140, 142, 143, 145, 147, 148, 150, 151, 153, 155, 156, 158

Offset

1,1

Links

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

Example

See A186223.

Mathematica

(* Program for adjusted rank sequences as described at A186219 *)
d=-1/2; u=1/2; v=1/2; w=0; x=3/2; y=-1/2; z=0; (* triangular & pentagonal *)
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}]  (* A186225 *)
Table[b[n], {n, 1, 100}]  (* A186226 *)

Crossrefs

A186219, A186223, A186224, A186226.

Sequence in context: A024913 A284934 A320928 * A353130 A050172 A191877

Adjacent sequences: A186222 A186223 A186224 * A186226 A186227 A186228

Keyword

nonn

Author

Clark Kimberling, Feb 15 2011

Status

approved