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A191728 Dispersion of A047209, (numbers >1 and congruent to 1 or 4 mod 5), by antidiagonals. 20
1, 4, 2, 11, 6, 3, 29, 16, 9, 5, 74, 41, 24, 14, 7, 186, 104, 61, 36, 19, 8, 466, 261, 154, 91, 49, 21, 10, 1166, 654, 386, 229, 124, 54, 26, 12, 2916, 1636, 966, 574, 311, 136, 66, 31, 13, 7291, 4091, 2416, 1436, 779, 341, 166, 79, 34, 15, 18229, 10229 (list; table; graph; refs; listen; history; text; internal format)
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)

...

For further information about these 20 dispersions, see A191722.

...

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....4....11...29....74

2....6....16...41....104

3....9....24...61....154

5....14...36...91....229

7....19...49...124...311

8....21...54...136...341

MATHEMATICA

(* Program generates the dispersion array t of the increasing sequence f[n] *)

r = 40; r1 = 12;  c = 40; c1 = 12;

a=4; 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}]  (* A047209 *)

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}]] (* A191728 *)

Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191728  *)

CROSSREFS

Cf. A047222, A047209, A191738, A191722, A191426.

Sequence in context: A188128 A091484 A163544 * A191434 A163918 A318784

Adjacent sequences:  A191725 A191726 A191727 * A191729 A191730 A191731

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jun 13 2011

STATUS

approved

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Last modified February 18 00:28 EST 2020. Contains 332006 sequences. (Running on oeis4.)