A186322 -id:A186322 - cp's OEIS frontend

A186323 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 heptagonal numbers. Complement of A186322.

1, 4, 7, 9, 12, 14, 17, 20, 22, 25, 27, 30, 33, 35, 38, 40, 43, 45, 48, 51, 53, 56, 58, 61, 64, 66, 69, 71, 74, 76, 79, 82, 84, 87, 89, 92, 95, 97, 100, 102, 105, 107, 110, 113, 115, 118, 120, 123, 125, 128, 131, 133, 136, 138, 141, 144, 146, 149, 151, 154, 156, 159, 162, 164, 167, 169, 172, 175, 177, 180, 182, 185, 187, 190, 193, 195, 198, 200, 203, 206, 208, 211, 213

Offset: 1

Clark Kimberling, Feb 17 2011

nonn

			First, write
1..4...9..16....25...36...49...64.. (squares)
1....7.......18....34........55.... (heptagonal)
Replace each number by its rank, where ties are settled by ranking the square number after the heptagonal:
a=(2,3,5,6,8,10,11,13,...)=A186322
b=(1,4,7,9,12,15,17,20,...)=A186323.

Cf. A186320, A186321, A186322.

Mathematica
```
(See A186322.)
```

A186320 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 squares and heptagonal numbers. Complement of A186321.

Original entry on oeis.org

1, 3, 5, 6, 8, 10, 11, 13, 14, 16, 18, 19, 21, 23, 24, 26, 28, 29, 31, 32, 34, 36, 37, 39, 41, 42, 44, 46, 47, 49, 50, 52, 54, 55, 57, 59, 60, 62, 63, 65, 67, 68, 70, 72, 73, 75, 77, 78, 80, 81, 83, 85, 86, 88, 90, 91, 93, 94, 96, 98, 99, 101, 103, 104, 106, 108, 109, 111, 112, 114, 116, 117, 119, 121, 122, 124, 125, 127, 129, 130, 132, 134, 135, 137, 139, 140, 142, 143, 145, 147, 148, 150, 152, 153, 155, 157, 158, 160, 161, 163

Offset: 1

Clark Kimberling, Feb 17 2011

nonn

			First, write
1..4...9..16....25...36...49...64.. (squares)
1....7.......18....34........55.... (heptagonal)
Replace each number by its rank, where ties are settled by ranking the square number before the heptagonal:
a=(1,3,5,6,8,10,11,13,...)=A186320
b=(2,4,7,9,12,15,17,20,...)=A186321.

Cf. A186219, A186321, A186322, A186323,

A000290 (squares), A000566 (heptagonal numbers).

(* adjusted joint ranking; general formula *)
d=1/2; u=1; v=0; w=0; x=5/2; y=-3/2; 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}]  (* A186320 *)
Table[b[n], {n, 1, 100}]  (* A186321 *)

A186321 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 squares and heptagonal numbers. Complement of A186320.

Original entry on oeis.org

2, 4, 7, 9, 12, 15, 17, 20, 22, 25, 27, 30, 33, 35, 38, 40, 43, 45, 48, 51, 53, 56, 58, 61, 64, 66, 69, 71, 74, 76, 79, 82, 84, 87, 89, 92, 95, 97, 100, 102, 105, 107, 110, 113, 115, 118, 120, 123, 126, 128, 131, 133, 136, 138, 141, 144, 146, 149, 151, 154, 156, 159, 162, 164, 167, 169, 172, 175, 177, 180, 182, 185, 187, 190, 193, 195, 198, 200

Offset: 1

Clark Kimberling, Feb 17 2011

nonn

			First, write
1..4...9..16....25...36...49...64.. (squares)
1....7.......18....34........55.... (heptagonal)
Replace each number by its rank, where ties are settled by ranking the square number before the heptagonal:
a=(1,3,5,6,8,10,11,13,...)=A186320
b=(2,4,7,9,12,15,17,20,...)=A186321.

Cf. A186320, A186322, A186323.

Mathematica
```
(See A186320.)
```

cp's OEIS Frontend

A186323 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 heptagonal numbers. Complement of A186322.

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Mathematica

A186320 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 squares and heptagonal numbers. Complement of A186321.

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Author

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Mathematica

A186321 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 squares and heptagonal numbers. Complement of A186320.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica