A186344 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 pentagonal numbers and the octagonal numbers. Complement of A186345.

2, 3, 5, 7, 8, 10, 12, 13, 15, 17, 19, 20, 22, 24, 25, 27, 29, 30, 32, 34, 36, 37, 39, 41, 42, 44, 46, 48, 49, 51, 53, 54, 56, 58, 59, 61, 63, 65, 66, 68, 70, 71, 73, 75, 77, 78, 80, 82, 83, 85, 87, 88, 90, 92, 94, 95, 97, 99, 100, 102, 104, 106, 107, 109, 111, 112, 114, 116, 118, 119, 121, 123, 124, 126, 128, 129, 131, 133, 135, 136, 138, 140, 141, 143, 145, 147, 148, 150, 152, 153, 155, 157, 158, 160, 162, 164, 165, 167, 169, 170

Offset

1,1

Links

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

Example

First, write
1..5...12....22..35..... (pentagonal)
1....8....21........40.. (octagonal)
Then replace each number by its rank, where ties are settled by ranking the pentagonal number after the octagonal:
a=(2,3,5,7,8,10,12,13,15,....)=A186344
b=(1,4,6,9,11,14,16,19,21,...)=A186345.

Mathematica

(* adjusted joint ranking; general formula *)
d=-1/2; u=3/2; v=-1/2; w=0; x=3; y=-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}]  (* A186344 *)
Table[b[n], {n, 1, 100}]  (* A186345 *)

Crossrefs

Cf. A186342, A186343, A186345.

Sequence in context: A047222 A028763 A285977 * A186317 A285077 A143826

Adjacent sequences: A186341 A186342 A186343 * A186345 A186346 A186347

Keyword

nonn

Author

Clark Kimberling, Feb 18 2011

Status

approved