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A186275 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 octagonal numbers.  Complement of A186276. 3
2, 3, 4, 6, 7, 9, 10, 11, 13, 14, 16, 17, 18, 20, 21, 23, 24, 25, 27, 28, 30, 31, 32, 34, 35, 37, 38, 39, 41, 42, 44, 45, 47, 48, 49, 51, 52, 54, 55, 56, 58, 59, 61, 62, 63, 65, 66, 68, 69, 70, 72, 73, 75, 76, 77, 79, 80, 82, 83, 85, 86, 87, 89, 90, 92, 93, 94, 96, 97, 99, 100, 101, 103, 104, 106, 107, 108, 110, 111, 113, 114, 116, 117, 118, 120, 121, 123, 124, 125, 127, 128, 130, 131, 132, 134, 135, 137, 138, 139, 141 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A186159.

LINKS

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

EXAMPLE

First, write the triangular and octagonal numbers:

1..3..6.....10..15..21..28

1........8..........21......

Then replace each by its rank, where ties are settled by ranking the triangular number after the octagonal:

a=(2,3,4,6,7,9,10,11,13,...)=A186275.

b=(1,5,8,12,15,19,22,26,...)=A186276.

MATHEMATICA

(* adjusted joint ranking; general formula *)

d=-1/2; u=1/2; 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}] (* A186275 *)

Table[b[n], {n, 1, 100}] (* A186276 *)

CROSSREFS

Cf. A186159, A186274, A186276.

Sequence in context: A070124 A059097 A047301 * A214857 A175320 A325597

Adjacent sequences:  A186272 A186273 A186274 * A186276 A186277 A186278

KEYWORD

nonn

AUTHOR

Clark Kimberling, Feb 16 2011

STATUS

approved

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Last modified September 26 06:16 EDT 2021. Contains 347664 sequences. (Running on oeis4.)