A191722 Dispersion of A008851, (numbers >1 and congruent to 0 or 1 mod 5), by antidiagonals.

1, 5, 2, 15, 6, 3, 40, 16, 10, 4, 101, 41, 26, 11, 7, 255, 105, 66, 30, 20, 8, 640, 265, 166, 76, 51, 21, 9, 1601, 665, 416, 191, 130, 55, 25, 12, 4005, 1665, 1041, 480, 326, 140, 65, 31, 13, 10015, 4165, 2605, 1201, 816, 351, 165, 80, 35, 14, 25040, 10415

Offset

1,2

Comments

For a background discussion of dispersions and their fractal sequences, see A191426. For dispersions of congruence sequences mod 3, mod 4, or mod 5, see A191655, A191663, A191667, A191702.

...

Suppose that {2,3,4,5,6} is partitioned as {x1, x2} and {x3,x4,x5}. Let S be the increasing sequence of numbers >1 and congruent to x1 or x2 mod 5, and let T be the increasing sequence of numbers >1 and congruent to x3 or x4 or x5 mod 5. There are 10 sequences in S, each matched by a (nearly) complementary sequence in T. Each of the 20 sequences generates a dispersion, as listed here:

...

A191722=dispersion of A008851 (0, 1 mod 5 and >1)

A191723=dispersion of A047215 (0, 2 mod 5 and >1)

A191724=dispersion of A047218 (0, 3 mod 5 and >1)

A191725=dispersion of A047208 (0, 4 mod 5 and >1)

A191726=dispersion of A047216 (1, 2 mod 5 and >1)

A191727=dispersion of A047219 (1, 3 mod 5 and >1)

A191728=dispersion of A047209 (1, 4 mod 5 and >1)

A191729=dispersion of A047221 (2, 3 mod 5 and >1)

A191730=dispersion of A047211 (2, 4 mod 5 and >1)

A191731=dispersion of A047204 (3, 4 mod 5 and >1)

...

A191732=dispersion of A047202 (2,3,4 mod 5 and >1)

A191733=dispersion of A047206 (1,3,4 mod 5 and >1)

A191734=dispersion of A032793 (1,2,4 mod 5 and >1)

A191735=dispersion of A047223 (1,2,3 mod 5 and >1)

A191736=dispersion of A047205 (0,3,4 mod 5 and >1)

A191737=dispersion of A047212 (0,2,4 mod 5 and >1)

A191738=dispersion of A047222 (0,2,3 mod 5 and >1)

A191739=dispersion of A008854 (0,1,4 mod 5 and >1)

A191740=dispersion of A047220 (0,1,3 mod 5 and >1)

A191741=dispersion of A047217 (0,1,2 mod 5 and >1)

...

EXCEPT for at most 2 initial terms (so that column 1 always starts with 1):

A191722 has 1st col A047202, all else A008851

A191723 has 1st col A047206, all else A047215

A191724 has 1st col A032793, all else A047218

A191725 has 1st col A047223, all else A047208

A191726 has 1st col A047205, all else A047216

A191727 has 1st col A047212, all else A047219

A191728 has 1st col A047222, all else A047209

A191729 has 1st col A008854, all else A047221

A191730 has 1st col A047220, all else A047211

A191731 has 1st col A047217, all else A047204

...

A191732 has 1st col A000851, all else A047202

A191733 has 1st col A047215, all else A047206

A191734 has 1st col A047218, all else A032793

A191735 has 1st col A047208, all else A047223

A191736 has 1st col A047216, all else A047205

A191737 has 1st col A047219, all else A047212

A191738 has 1st col A047209, all else A047222

A191739 has 1st col A047221, all else A008854

A191740 has 1st col A047211, all else A047220

A191741 has 1st col A047204, all else A047217

...

Regarding the dispersions A191722-A191741, there are general formulas for sequences of the type "(a or b mod m)" and "(a or b or c mod m)" used in the relevant Mathematica programs.

Links

Ivan Neretin, Table of n, a(n) for n = 1..5050

Example

Northwest corner:
1....5....15...40...101
2....6....16...41...105
3....10...26...66...166
4....11...30...76...191
7....20...51...130..326
8....21...55...140..351

Mathematica

(* Program generates the dispersion array t of the increasing sequence f[n] *)
r = 40; r1 = 12;  c = 40; c1 = 12;
a=5; b=6; m[n_]:=If[Mod[n, 2]==0, 1, 0];
f[n_]:=a*m[n+1]+b*m[n]+5*Floor[(n-1)/2]
Table[f[n], {n, 1, 30}]  (* A008851 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191722 *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191722  *)

Crossrefs

Cf. A047202, A008851, A191732, A191702, A191426.

Sequence in context: A265434 A189236 A341515 * A191435 A128142 A213550

Adjacent sequences: A191719 A191720 A191721 * A191723 A191724 A191725

Keyword

nonn,tabl

Author

Clark Kimberling, Jun 13 2011

Status

approved