

A186227


Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) before g(j) when f(i)=g(j), where f and g are the triangular numbers and heptagonal numbers. Complement of A186228.


4



1, 3, 4, 6, 7, 9, 10, 12, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 43, 45, 46, 48, 49, 51, 52, 54, 55, 56, 58, 59, 61, 62, 64, 65, 67, 68, 69, 71, 72, 74, 75, 77, 78, 80, 81, 83, 84, 85, 87, 88, 90, 91, 93, 94, 96, 97, 98, 100, 101, 103, 104, 106, 107, 109, 110, 111, 113, 114, 116, 117, 119, 120, 122, 123, 124, 126, 127, 129, 130, 132, 133, 135, 136, 138, 139, 140, 142, 143, 145
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OFFSET

1,2


COMMENTS

See A186219 for a general discussion of adjusted joint rank sequences.


LINKS

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


EXAMPLE

First, write
1..3..6..10..15..21..28..36..45... (triangular)
1.......7......18......34.......55... (heptagonal)
Then replace each number by its rank, where ties are settled by ranking the triangular number before the heptagonal:
a=(1,3,4,6,7,9,10,12,...), A186227.
b=(2,5,8,11,15,18,21,...), A186228.


MATHEMATICA

(* adjusted joint ranking; general formula *)
d=1/2; u=1/2; v=1/2; w=0; x=5/2; y=3/2; 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}] (* A186227 *)
Table[b[n], {n, 1, 100}] (* A186228 *)


CROSSREFS

Cf. A186219, A186228, A186237, A186238,
Cf. A000217 (triangular numbers)
Cf. A000566 (heptagonal numbers)
Sequence in context: A246443 A186495 A184746 * A258048 A185543 A026322
Adjacent sequences: A186224 A186225 A186226 * A186228 A186229 A186230


KEYWORD

nonn


AUTHOR

Clark Kimberling, Feb 16 2011


STATUS

approved



