

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.


4



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
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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+wzd)+y^2)^(1/2);
a[n_]:=n+Floor[h[n]/(2x)];
k[n_]:=v+(4u(x*n^2+y*n+zw+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



