login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A274630 Square array T(n,k) (n>=1, k>=1) read by antidiagonals upwards in which the number entered in a square is the smallest positive number that is different from the numbers already filled in that are queens' or knights' moves away from that square. 7
1, 2, 3, 4, 5, 6, 3, 7, 8, 2, 5, 1, 9, 4, 7, 6, 2, 10, 11, 1, 5, 7, 4, 12, 6, 3, 9, 8, 8, 9, 11, 13, 2, 10, 6, 4, 10, 12, 1, 3, 4, 7, 13, 11, 9, 9, 6, 2, 5, 8, 1, 12, 14, 3, 10, 11, 13, 3, 7, 6, 14, 9, 5, 1, 12, 15, 12, 8, 4, 14, 9, 11, 10, 3, 15, 2, 7, 13, 13, 10, 5, 1, 12, 15, 2, 16, 6, 4, 8, 14, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If we only worry about queens' moves then we get the array in A269526.

Presumably, as in A269526, every column, every row, and every diagonal is a permutation of the natural numbers.

The knights only affect the squares in their immediate neighborhood, so this array will have very similar properties to A269526. The most noticeable difference is that the first column is no longer A000027, it is now A274631.

A piece that can move like a queen or a knight is known as a Maharaja.  If we subtract 1 from the entries here we obtain A308201. - N. J. A. Sloane, Jun 30 2019

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..10010

EXAMPLE

The array begins:

1, 3, 6, 2, 7, 5, 8, 4, 9, 10, 15, 13, 11, 18, 12, 20, 16, 22, ...

2, 5, 8, 4, 1, 9, 6, 11, 3, 12, 7, 14, 17, 15, 10, 13, 19, 24, ...

4, 7, 9, 11, 3, 10, 13, 14, 1, 2, 8, 5, 6, 16, 22, 17, 21, 12, ...

3, 1, 10, 6, 2, 7, 12, 5, 15, 4, 16, 20, 13, 9, 11, 14, 25, 8, ...

5, 2, 12, 13, 4, 1, 9, 3, 6, 11, 10, 17, 19, 8, 7, 15, 23, 29, ...

6, 4, 11, 3, 8, 14, 10, 16, 13, 1, 2, 7, 15, 5, 24, 21, 9, 28, ...

7, 9, 1, 5, 6, 11, 2, 12, 8, 14, 3, 21, 23, 22, 4, 27, 18, 30, ...

8, 12, 2, 7, 9, 15, 1, 19, 4, 5, 6, 10, 18, 3, 26, 23, 11, 31, ...

10, 6, 3, 14, 12, 4, 5, 9, 11, 7, 1, 8, 16, 13, 2, 24, 28, 20, ...

9, 13, 4, 1, 10, 2, 7, 18, 12, 3, 17, 19, 24, 14, 20, 5, 8, 6, ...

11, 8, 5, 9, 13, 3, 15, 1, 2, 6, 20, 18, 10, 4, 17, 7, 12, 14, ...

12, 10, 7, 18, 11, 6, 4, 8, 14, 9, 5, 15, 21, 2, 16, 26, 3, 13, ...

13, 15, 17, 12, 14, 16, 18, 7, 10, 22, 11, 3, 8, 19, 23, 9, 2, 1, ...

14, 11, 19, 8, 5, 20, 3, 2, 16, 13, 12, 25, 4, 10, 6, 18, 7, 15, ...

16, 18, 21, 10, 15, 13, 11, 17, 5, 8, 9, 6, 7, 30, 25, 28, 20, 19, ...

15, 20, 13, 17, 16, 12, 19, 6, 7, 24, 18, 11, 28, 23, 14, 22, 5, 36, ...

17, 14, 22, 19, 18, 8, 20, 10, 23, 15, 4, 1, 3, 24, 13, 16, 33, 9, ...

18, 16, 23, 24, 25, 26, 14, 13, 17, 19, 22, 9, 5, 6, 8, 10, 15, 27, ...

...

Look at the entry in the second cell in row 3. It can't be a 1, because the 1 in cell(1,2) is a knight's move away, it can't be a 2, 3, 4, or 5, because it is adjacent to cells containing these numbers, and there is a 6 in cell (1,3) that is a knight's move away. The smallest free number is therefore 7.

MAPLE

# Based on Alois P. Heinz's program for A269526

A:= proc(n, k) option remember; local m, s;

         if n=1 and k=1 then 1

       else s:= {seq(A(i, k), i=1..n-1),

                 seq(A(n, j), j=1..k-1),

                 seq(A(n-t, k-t), t=1..min(n, k)-1),

                 seq(A(n+j, k-j), j=1..k-1)};

# add knights moves

if n >= 3            then s:={op(s), A(n-2, k+1)}; fi;

if n >= 3 and k >= 2 then s:={op(s), A(n-2, k-1)}; fi;

if n >= 2 and k >= 3 then s:={op(s), A(n-1, k-2)}; fi;

if            k >= 3 then s:={op(s), A(n+1, k-2)}; fi;

            for m while m in s do od; m

         fi

     end:

[seq(seq(A(1+d-k, k), k=1..d), d=1..15)];

MATHEMATICA

A[n_, k_] := A[n, k] = Module[{m, s}, If[n==1 && k==1, 1, s = Join[Table[ A[i, k], {i, 1, n-1}], Table[A[n, j], {j, 1, k-1}], Table[A[n-t, k-t], {t, 1, Min[n, k]-1}], Table[A[n+j, k-j], {j, 1, k-1}]] // Union; If[n >= 3, AppendTo[s, A[n-2, k+1]] // Union ]; If[n >= 3 && k >= 2, AppendTo[s, A[n-2, k-1]] // Union]; If[n >= 2 && k >= 3, AppendTo[s, A[n-1, k-2]] // Union]; If[k >= 3, AppendTo[s, A[n+1, k-2]] // Union]; For[m = 1, MemberQ[s, m], m++]; m]]; Table[A[1+d-k, k], {d, 1, 15}, {k, 1, d}] // Flatten (* Jean-Fran├žois Alcover, Mar 14 2017, translated from Maple *)

CROSSREFS

Cf. A269526, A000027.

For first column, row, and main diagonal see A274631, A274632, A274633.

See A308883 for position of 1 in column n.

See A308201 for an essentially identical array.

Sequence in context: A195153 A328764 A323081 * A278058 A320115 A319994

Adjacent sequences:  A274627 A274628 A274629 * A274631 A274632 A274633

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane following a suggestion from Joseph G. Rosenstein, Jul 07 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 13 09:54 EST 2019. Contains 329968 sequences. (Running on oeis4.)