A165403 -id:A165403 - cp's OEIS frontend

A163904 Array A(i,j): Cycle size of each A054238(i,j) in permutation A163355, listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...

1, 1, 2, 6, 2, 6, 3, 3, 6, 3, 1, 6, 6, 3, 4, 3, 3, 3, 6, 8, 8, 1, 3, 4, 3, 4, 4, 2, 1, 2, 2, 2, 2, 2, 2, 2, 6, 2, 4, 4, 4, 4, 8, 2, 6, 6, 6, 2, 4, 4, 8, 8, 4, 6, 6, 12, 6, 12, 2, 4, 8, 4, 4, 12, 6, 18, 6, 6, 12, 6, 2, 4, 8, 4, 6, 12, 18, 6, 3, 12, 18, 6, 9, 2, 2, 8, 6, 6, 12, 18, 3, 3, 6, 18, 18

Offset: 0

Antti Karttunen, Sep 19 2009

			The top left 8x8 corner of this array:
1 1 6 3 1 3 1 1
2 2 3 6 3 3 2 2
6 6 6 3 4 2 4 2
3 3 6 3 2 4 4 2
4 8 4 2 4 4 4 2
8 4 2 4 8 8 4 2
2 2 8 8 4 8 2 2
2 2 4 4 4 8 2 2

A. Karttunen, Table of n, a(n) for n = 0..32895

a(n) = A163890(A054238(n)) = A163890(A163357(n)). Positions of 1's: A165403. See also A163898, A163899.

A163898 Array A(i,j) giving the square of distance from (i,j) to the location where A054238(i,j) is situated in array A163357(i,j), listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...

Original entry on oeis.org

0, 0, 1, 8, 1, 4, 18, 5, 2, 9, 0, 5, 2, 5, 16, 2, 1, 2, 9, 10, 25, 0, 1, 4, 9, 16, 17, 36, 0, 1, 4, 9, 16, 25, 36, 49, 128, 1, 2, 1, 10, 9, 10, 25, 64, 162, 113, 4, 5, 18, 5, 4, 5, 50, 81, 128, 113, 100, 9, 10, 5, 10, 1, 64, 65, 100, 128, 113, 100, 89, 16, 17, 20, 25, 64, 81, 100

Offset: 0

Antti Karttunen, Sep 19 2009

			The top left 8 X 8 corner of this array:
   0  0  8 18  0  2  0  0
   1  1  5  5  1  1  1  1
   4  2  2  2  4  4  2  4
   9  5  9  9  9  1  5  9
  16 10 16 16 10 18 10 16
  25 17 25  9  5  5 17 25
  36 36 10  4 10 20 36 36
  49 25  5  1 25 29 25 49

A. Karttunen, Table of n, a(n) for n = 0..32895

a(n) = A163900(A054238(n)). Positions of zeros: A165403. See also A163899, A163904.

A163899 Array A(i,j) giving the square of distance from (i,j) to the location where A163357(i,j) is situated in array A054238(i,j), listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...

Original entry on oeis.org

0, 0, 1, 9, 1, 8, 9, 2, 5, 18, 0, 2, 4, 5, 25, 1, 2, 5, 2, 20, 29, 0, 1, 5, 9, 17, 10, 36, 0, 1, 4, 9, 16, 25, 36, 49, 225, 1, 4, 2, 16, 10, 5, 25, 128, 225, 170, 4, 1, 17, 10, 5, 18, 113, 162, 196, 170, 125, 9, 16, 25, 5, 10, 128, 113, 149, 225, 170, 125, 90, 16, 9, 4, 1, 128

Offset: 0

Antti Karttunen, Sep 19 2009

			The top left 8x8 corner of this array:
+0 +0 +9 +9 +0 +1 +0 +0
+1 +1 +2 +2 +2 +1 +1 +1
+8 +5 +4 +5 +5 +4 +4 +4
18 +5 +2 +9 +9 +2 +1 +9
25 20 17 16 16 17 16 16
29 10 25 10 10 25 +9 25
36 36 +5 +5 +5 +4 36 36
49 25 18 10 +1 10 25 49

A. Karttunen, Table of n, a(n) for n = 0..32895

a(n) = A163900(A163357(n)). Positions of zeros: A165403. See also A163898, A163904.

A165404 The positions of zeros in the top row of A163898 (and A163899).

Original entry on oeis.org

0, 1, 4, 6, 7, 16, 18, 19, 24, 25, 28, 30, 31, 64, 66, 67, 72, 73, 76, 78, 79, 96, 97, 100, 102, 103, 112, 114, 115, 120, 121, 124, 126, 127, 256, 258, 259, 264, 265, 268, 270, 271, 288, 289, 292, 294, 295, 304, 306, 307, 312, 313, 316, 318, 319, 384, 385, 388

Offset: 0

Antti Karttunen, Sep 19 2009

nonn

Equivalently, the positions of ones in the top row of A163904.

A. Karttunen, Table of n, a(n) for n = 0..609

a(n) = A025581(A165403(n)). Same sequence in binary: A165406. For n>0, A147600(n-1) seems to give the number of terms with binary width n. See also A163901.

cp's OEIS Frontend

A163904 Array A(i,j): Cycle size of each A054238(i,j) in permutation A163355, listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...

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A163898 Array A(i,j) giving the square of distance from (i,j) to the location where A054238(i,j) is situated in array A163357(i,j), listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...

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A163899 Array A(i,j) giving the square of distance from (i,j) to the location where A163357(i,j) is situated in array A054238(i,j), listed antidiagonally as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...

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A165404 The positions of zeros in the top row of A163898 (and A163899).

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