cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 28 results. Next

A199134 Indices of Greedy Queens (see A065188) below main diagonal.

Original entry on oeis.org

4, 5, 10, 11, 13, 15, 20, 21, 26, 27, 29, 31, 34, 38, 40, 42, 43, 49, 50, 54, 56, 58, 59, 64, 67, 69, 71, 75, 77, 78, 80, 85, 86, 90, 91, 95, 99, 101, 102, 104, 108, 111, 113, 116, 117, 120, 123, 128, 129, 132, 133, 136, 141, 143, 144, 146, 151, 152, 154, 156, 160
Offset: 1

Views

Author

Wouter Meeussen, Nov 04 2011

Keywords

Comments

The word "below" in the definition is somewhat ambiguous. More precisely, this is the list of n such that A065188(n) < n. - N. J. A. Sloane, Aug 18 2016
For Greedy Queens that do not attack along antidiagonals, the analogous sequence of indices is A026352.

Examples

			Greedy Queens take positions (1,1) (2,3) (3,5) (4,2) (5,4) (6,9) ... and the 4th and 5th are below the main diagonal, so a(1)=4 and a(2)=5.

Links

Crossrefs

Cf. A065188, A026352, A275893 (another version).
A275884 is the complementary sequence.
For runs see A275885, A275886.

Programs

  • Mathematica
    <2+Floor[k*GoldenRatio],And[l>3+Floor[k/GoldenRatio],l

A275884 Indices of Greedy Queens (see A065188) on or above the main diagonal.

Original entry on oeis.org

1, 2, 3, 6, 7, 8, 9, 12, 14, 16, 17, 18, 19, 22, 23, 24, 25, 28, 30, 32, 33, 35, 36, 37, 39, 41, 44, 45, 46, 47, 48, 51, 52, 53, 55, 57, 60, 61, 62, 63, 65, 66, 68, 70, 72, 73, 74, 76, 79, 81, 82, 83, 84, 87, 88, 89, 92, 93, 94, 96, 97, 98, 100, 103, 105, 106, 107, 109, 110, 112, 114, 115, 118, 119
Offset: 1

Views

Author

N. J. A. Sloane, Aug 18 2016

Keywords

Comments

The word "above" in the definition is somewhat ambiguous. More precisely, this is the list of n such that A065188(n) >= n.
If one looks at the graph of A065188, the points appear to lie roughly on two lines, of slopes phi (the golden ratio) and 1/phi. The points in the present sequence appear to fall on the line of slope phi. That is, it is appears that A065188(a(n))/a(n) -> phi as n -> oo.

Links

Crossrefs

Cf. A065188, A275894 (another version). Complement of A199134.
For runs see A275885, A275886.

A065189 "Greedy Queens" permutation of the natural numbers, inverse of A065188.

Original entry on oeis.org

1, 4, 2, 5, 3, 10, 13, 11, 6, 15, 7, 20, 8, 21, 9, 26, 29, 27, 12, 31, 34, 14, 38, 40, 16, 43, 17, 42, 18, 49, 19, 50, 54, 56, 22, 59, 23, 58, 24, 64, 25, 67, 69, 71, 28, 75, 77, 30, 80, 78, 32, 85, 33, 86, 90, 35, 91, 36, 95, 37, 99, 101, 39, 104, 102, 41, 108, 111, 113, 44
Offset: 1

Views

Author

Antti Karttunen, Oct 19 2001

Keywords

Links

Crossrefs

Cf. A065188, A269526.

A276325 Diagonal indices of Greedy Queens (see A065188).

Original entry on oeis.org

0, -1, 2, -2, 1, -3, 4, -4, 3, 6, -5, -6, 5, -7, 8, 7, -8, -9, 10, -10, 9, 12, -11, -12, 11, 13, -13, -14, 15, -15, 16, -16, 17, 14, -17, -18, 19, 18, -19, -20, 21, 22, -21, -22, 23, 20, -23, -24, 24, -25, 25, 26, -26, 27, -27, -28, 29, -29, 30, -30, 28, 31
Offset: 1

Views

Author

Alois P. Heinz, Aug 30 2016

Keywords

Comments

a(n) is the index of the diagonal of the n-th queen. The main diagonal has index 0, upper (lower) diagonals have positive (negative) indices.

Examples

			The first queen is in the main diagonal, the second queen is in the first lower diagonal, the third queen is in the second upper diagonal, ... :
:
:  Q\\\\ ...
:  \\\Q\ ...
:  \Q\\\ ...
:  \\\\Q ...
:  \\Q\\ ...
:  \\\\\ ...
:  .....

Links

Crossrefs

Cf. A065188, A276324, A275901, A275902.

Programs

  • Maple
    # Maple program from N. J. A. Sloane, Oct 03 2016
# To get 10000 terms of A275902 (xx), A275901 (yy), A276783 (ss), -A276325 (dd)
M1:=100000; M2:=22000; M3:=10000;
xx:=Array(0..M1,0); yy:=Array(0..M1,0); ss:=Array(0..M1,0); dd:=Array(0..M1,0);
xx[0]:=0; yy[0]:=0; ss[0]:=0; dd[0]:=0;
for n from 1 to M2 do
sw:=-1;
   for s from ss[n-1]+1 to M2 do
      for i from 0 to s do
         x:=s-i; y:=i;
         if not member(x,xx,'p') and
            not member(y,yy,'p') and
            not member(x-y,dd,'p') then sw:=1; break; fi;
      od:  # od i
if sw=1 then break; fi;
   od: # od s
  if sw=-1 then lprint("error, n=",n); break; fi;
xx[n]:=x; yy[n]:=y; ss[n]:=x+y; dd[n]:=x-y;
od: # od n
[seq(xx[i],i=0..M3)]:
[seq(yy[i],i=0..M3)]:
[seq(ss[i],i=0..M3)]:
[seq(dd[i],i=0..M3)]:

Formula

Equals A275901 - A275902.

A275897 Read the infinite chessboard underlying A065188 by successive antidiagonals and record when the queens are encountered. Here the rows and columns are indexed starting at 0 (as in A275895).

Original entry on oeis.org

0, 7, 13, 23, 32, 96, 114, 142, 163, 183, 197, 261, 290, 446, 484, 581, 608, 795, 845, 919, 972, 1018, 1052, 1194, 1255, 1464, 1561, 1733, 1807, 1914, 1992, 2104, 2320, 2387, 2583, 2955, 3051, 3289, 3352, 3602, 3708, 3971, 4039, 4313, 4429, 4522, 4596, 5088, 5316, 5605, 5844, 6173, 6371
Offset: 1

Views

Author

N. J. A. Sloane, Aug 23 2016, following a suggestion from David A. Corneth

Keywords

Examples

			The second queen appears in the fourth antidiagonal at position 7 (calling the top left square square 0):
Qxxx
xxxQ
xQxx
xxxx
so a(2) = 7.

Links

Crossrefs

Cf. A065188, A275895, A275898.

Programs

  • Maple
    # Let b8 be a list of the terms of A065188.
ts:=[];
for n from 1 to 130 do
ta:=b8[n];
tb:=n-1+(ta+n-2)*(ta+n-1)/2;
ts:=[op(ts),tb]; od:
tt:=sort(ts); # A275897
tu:=map(x->x+1,tt); # A275898
  • Mathematica
    b8 = Cases[Import["https://oeis.org/A065188/b065188.txt", "Table"], {, }][[All, 2]];
ts = {};
For[n = 1, n <= 130, n++, ta = b8[[n]]; tb = n - 1 + (ta + n - 2)*(ta + n - 1)/2; ts = Append[ts, tb]];
Sort[ts] (* Jean-François Alcover, Feb 27 2020, from Maple *)

A275899 Following the successive antidiagonals in A065188, let the n-th queen appear in square (x(n),y(n)); sequence gives x(n).

Original entry on oeis.org

1, 2, 4, 3, 5, 6, 10, 7, 11, 13, 8, 9, 15, 12, 20, 21, 14, 16, 26, 17, 27, 29, 18, 19, 31, 34, 22, 23, 38, 24, 40, 25, 43, 42, 28, 30, 49, 50, 32, 33, 54, 56, 35, 36, 59, 58, 37, 39, 64, 41, 67, 69, 44, 71, 45, 46, 75, 47, 77, 48, 78, 80, 51, 52, 85, 53, 86, 55, 90, 91, 57, 95, 60, 61, 99, 62, 101, 63
Offset: 1

Views

Author

N. J. A. Sloane, Aug 24 2016

Keywords

Comments

See A275900 for y(n).
This is a permutation of the natural numbers.
This assumes the indexing starts at 1. See A275901, A275902 if the indexing begins at 0.

Links

Crossrefs

Cf. A065188, A275900, A275901, A275902.

Programs

  • Maple
    # To get the coordinates of queens in order of appearance; b8[] has list of terms of A065188
M:=7500; c1:=[]; c2:=[];
t1:=[seq(n+b8[n],n=1..M)];
t2:=sort(t1);
for n from 1 to M do
i:=t2[n]; member(i,t1,'j');
c1:=[op(c1),j]; c2:=[op(c2),b8[j]];
od:
c3:=map(x->x-1,c1):
c4:=map(x->x-1,c2):
[seq(c1[n],n=1..80)]; # A275899
[seq(c2[n],n=1..80)]; # A275900
[seq(c3[n],n=1..80)]; @ A275901
[seq(c4[n],n=1..80)]; @ A275902

A275900 Following the successive antidiagonals in A065188, let the n-th queen appear in square (x(n),y(n)); sequence gives y(n).

Original entry on oeis.org

1, 3, 2, 5, 4, 9, 6, 11, 8, 7, 13, 15, 10, 19, 12, 14, 22, 25, 16, 27, 18, 17, 29, 31, 20, 21, 35, 37, 23, 39, 24, 41, 26, 28, 45, 48, 30, 32, 51, 53, 33, 34, 56, 58, 36, 38, 60, 63, 40, 66, 42, 43, 70, 44, 72, 74, 46, 76, 47, 78, 50, 49, 82, 84, 52, 86, 54, 89, 55, 57, 92, 59, 96, 98, 61, 100, 62, 102
Offset: 1

Views

Author

N. J. A. Sloane, Aug 24 2016

Keywords

Comments

See A275899 for x(n).
This is a permutation of the natural numbers.
This assumes the indexing starts at 1. See A275901, A275902 if the indexing begins at 0.

Links

Crossrefs

Cf. A065188, A275899, A275901, A275902.

Programs

A276324 Antidiagonal indices of Greedy Queens (see A065188).

Original entry on oeis.org

1, 4, 5, 7, 8, 14, 15, 17, 18, 19, 20, 23, 24, 30, 31, 34, 35, 40, 41, 43, 44, 45, 46, 49, 50, 54, 56, 59, 60, 62, 63, 65, 68, 69, 72, 77, 78, 81, 82, 85, 86, 89, 90, 93, 94, 95, 96, 101, 103, 106, 108, 111, 113, 114, 116, 119, 120, 122, 123, 125, 127, 128
Offset: 1

Views

Author

Alois P. Heinz, Aug 30 2016

Keywords

Comments

a(n) is the index of the antidiagonal of the n-th queen.

Examples

			The first queen is in the first antidiagonal, the second queen is in the fourth antidiagonal, ... .  The antidiagonals with indices 2, 3, 6, 9, ... do not contain a queen:
:
:  Q//// ...
:  ///Q/ ...
:  /Q/// ...
:  ////Q ...
:  //Q// ...
:  ///// ...
:  .....

Links

Crossrefs

Cf. A065188, A276325.

A275890 a(n) is the number of i <= n such that A065188(i) >= i.

Original entry on oeis.org

1, 2, 3, 3, 3, 4, 5, 6, 7, 7, 7, 8, 8, 9, 9, 10, 11, 12, 13, 13, 13, 14, 15, 16, 17, 17, 17, 18, 18, 19, 19, 20, 21, 21, 22, 23, 24, 24, 25, 25, 26, 26, 26, 27, 28, 29, 30, 31, 31, 31, 32, 33, 34, 34, 35, 35, 36, 36, 36, 37, 38, 39, 40, 40, 41, 42, 42, 43, 43, 44, 44, 45, 46, 47, 47, 48, 48, 48, 49, 49
Offset: 1

Views

Author

N. J. A. Sloane, Aug 20 2016

Keywords

Comments

Counts terms of A065188 that are on or below the main diagonal.

Crossrefs

Cf. A065188, A275891, A275892.

A275891 a(n) is the number of i <= n such that A065188(i) < i.

Original entry on oeis.org

0, 0, 0, 1, 2, 2, 2, 2, 2, 3, 4, 4, 5, 5, 6, 6, 6, 6, 6, 7, 8, 8, 8, 8, 8, 9, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 15, 15, 16, 17, 17, 17, 17, 17, 17, 18, 19, 19, 19, 19, 20, 20, 21, 21, 22, 23, 23, 23, 23, 23, 24, 24, 24, 25, 25, 26, 26, 27, 27, 27, 27, 28, 28, 29, 30, 30, 31, 31, 31, 31
Offset: 1

Views

Author

N. J. A. Sloane, Aug 20 2016

Keywords

Comments

Counts terms of A065188 that are above the main diagonal.

Crossrefs

Cf. A065188, A275890, A275892.
Showing 1-10 of 28 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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