A082793 -id:A082793 - cp's OEIS frontend

A191734 Dispersion of A032793, (numbers >1 and congruent to 1 or 2 or 4 mod 5), by antidiagonals.

1, 2, 3, 4, 6, 5, 7, 11, 9, 8, 12, 19, 16, 14, 10, 21, 32, 27, 24, 17, 13, 36, 54, 46, 41, 29, 22, 15, 61, 91, 77, 69, 49, 37, 26, 18, 102, 152, 129, 116, 82, 62, 44, 31, 20, 171, 254, 216, 194, 137, 104, 74, 52, 34, 23, 286, 424, 361, 324, 229, 174, 124, 87

Offset: 1

Clark Kimberling, Jun 14 2011

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.

			Northwest corner:
1....2....4....7...12
3....6....11...19...32
5....9....16...27...46
8....14...24...41...69
10...17...29...49...82
13...22...37...62...104

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

Cf. A047218, A082793, A191722, , A191724, A191426.

(* Program generates the dispersion array t of the increasing sequence f[n] *)
r = 40; r1 = 12;  c = 40; c1 = 12;
a=2; b=4; c2=6; m[n_]:=If[Mod[n,3]==0,1,0];
f[n_]:=a*m[n+2]+b*m[n+1]+c2*m[n]+5*Floor[(n-1)/3]
Table[f[n], {n, 1, 30}]  (* A032793 *)
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}]] (* A191734 *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191734  *)

A082792 Smallest multiple of n beginning with 3.

Original entry on oeis.org

3, 30, 3, 32, 30, 30, 35, 32, 36, 30, 33, 36, 39, 308, 30, 32, 34, 36, 38, 300, 315, 308, 322, 312, 300, 312, 324, 308, 319, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 320, 328, 336, 301, 308, 315, 322, 329, 336, 343, 300, 306, 312, 318, 324, 330, 336, 342, 348, 354

Offset: 1

Amarnath Murthy, Apr 20 2003

a(n) is in {n, 2n, 3n, 4n, 5n, 6n, 7n, 8n, 11n, 12n, 13n, 14n, 15n, 21n, 22n, 23n}. - Charles R Greathouse IV, Mar 06 2011

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A082793, A082794, A082795, A082796.

Cf. A000030.

a082792 n = until ((== 3) . a000030) (+ n) n
-- Reinhard Zumkeller, Mar 27 2012

f[n_] := Block[{m = n}, While[ First@ IntegerDigits@ m != 3, m += n]; m]; Array[f, 59] (* Robert G. Wilson v, Mar 06 2011 *)

a(n)=forstep(k=n,23*n,n,if(Vec(Str(k))[1]=="3",return(k))) \\ Charles R Greathouse IV, Mar 06 2011

def a(n):
  kn = n
  while str(kn)[0] != '3': kn += n
  return kn
print([a(n) for n in range(1, 60)]) # Michael S. Branicky, Mar 30 2021

Corrected and extended by Sean A. Irvine, Mar 06 2011

cp's OEIS Frontend

A191734 Dispersion of A032793, (numbers >1 and congruent to 1 or 2 or 4 mod 5), by antidiagonals.

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A082792 Smallest multiple of n beginning with 3.

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