cp's OEIS Frontend

A191726 Dispersion of A047216, (numbers >1 and congruent to 1 or 2 mod 5), by antidiagonals.

%I A191726 #8 Oct 11 2017 16:47:43
%S A191726 1,2,3,6,7,4,16,17,11,5,41,42,27,12,8,102,106,67,31,21,9,256,266,167,
%T A191726 77,52,22,10,641,666,417,192,131,56,26,13,1602,1666,1042,481,327,141,
%U A191726 66,32,14,4006,4166,2606,1202,817,352,166,81,36,15,10016,10416
%N A191726 Dispersion of A047216, (numbers >1 and congruent to 1 or 2 mod 5), by antidiagonals.
%C A191726 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.
%C A191726 ...
%C A191726 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:
%C A191726 ...
%C A191726 A191722=dispersion of A008851 (0, 1 mod 5 and >1)
%C A191726 A191723=dispersion of A047215 (0, 2 mod 5 and >1)
%C A191726 A191724=dispersion of A047218 (0, 3 mod 5 and >1)
%C A191726 A191725=dispersion of A047208 (0, 4 mod 5 and >1)
%C A191726 A191726=dispersion of A047216 (1, 2 mod 5 and >1)
%C A191726 A191727=dispersion of A047219 (1, 3 mod 5 and >1)
%C A191726 A191728=dispersion of A047209 (1, 4 mod 5 and >1)
%C A191726 A191729=dispersion of A047221 (2, 3 mod 5 and >1)
%C A191726 A191730=dispersion of A047211 (2, 4 mod 5 and >1)
%C A191726 A191731=dispersion of A047204 (3, 4 mod 5 and >1)
%C A191726 ...
%C A191726 A191732=dispersion of A047202 (2,3,4 mod 5 and >1)
%C A191726 A191733=dispersion of A047206 (1,3,4 mod 5 and >1)
%C A191726 A191734=dispersion of A032793 (1,2,4 mod 5 and >1)
%C A191726 A191735=dispersion of A047223 (1,2,3 mod 5 and >1)
%C A191726 A191736=dispersion of A047205 (0,3,4 mod 5 and >1)
%C A191726 A191737=dispersion of A047212 (0,2,4 mod 5 and >1)
%C A191726 A191738=dispersion of A047222 (0,2,3 mod 5 and >1)
%C A191726 A191739=dispersion of A008854 (0,1,4 mod 5 and >1)
%C A191726 A191740=dispersion of A047220 (0,1,3 mod 5 and >1)
%C A191726 A191741=dispersion of A047217 (0,1,2 mod 5 and >1)
%C A191726 ...
%C A191726 For further information about these 20 dispersions, see A191722.
%C A191726 ...
%C A191726 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.
%H A191726 Ivan Neretin, <a href="/A191726/b191726.txt">Table of n, a(n) for n = 1..5050</a>
%e A191726 Northwest corner:
%e A191726 1....2....6....16....41
%e A191726 3....7....17...42....106
%e A191726 4....11...27...67....167
%e A191726 5....12...31...77....192
%e A191726 8....21...52...131...327
%e A191726 9....22...56...141...352
%t A191726 (* Program generates the dispersion array t of the increasing sequence f[n] *)
%t A191726 r = 40; r1 = 12;  c = 40; c1 = 12;
%t A191726 a=2; b=6; m[n_]:=If[Mod[n,2]==0,1,0];
%t A191726 f[n_]:=a*m[n+1]+b*m[n]+5*Floor[(n-1)/2]
%t A191726 Table[f[n], {n, 1, 30}]  (* A047216 *)
%t A191726 mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
%t A191726 rows = {NestList[f, 1, c]};
%t A191726 Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
%t A191726 t[i_, j_] := rows[[i, j]];
%t A191726 TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]] (* A191726 *)
%t A191726 Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191726  *)
%Y A191726 Cf. A047205, A047216, A191736, A191722, A191426.
%K A191726 nonn,tabl
%O A191726 1,2
%A A191726 _Clark Kimberling_, Jun 13 2011