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 1-8 of 8 results.

A184398 Ranks of (even i)+j*r, when all i+j*r are ranked; r=sqrt(2), i>=0, j>=0. Complement of A184397.

Original entry on oeis.org

1, 3, 4, 6, 8, 10, 11, 13, 16, 17, 19, 20, 23, 25, 27, 28, 30, 32, 34, 36, 38, 40, 42, 44, 45, 47, 49, 51, 54, 56, 57, 59, 61, 62, 64, 67, 69, 70, 73, 75, 76, 78, 81, 82, 84, 85, 88, 90, 91, 94, 97, 98, 100, 101, 104, 105, 107, 108, 111, 114, 115, 117, 119, 122, 123
Offset: 1

Views

Author

Clark Kimberling, Jan 12 2011

Keywords

Examples

			Writing (i,j) for i+j*r, the first 7 in the ranking are (0,0), (1,0), (0,1), (2,0), (1,1), (0,2), (3,0); the ranks where i is odd are 2,5,7 and the ranks where it is even are 1,3,4,6.

Crossrefs

Cf. A184397, A184399, A184400, A184401, A184402, A184403.

A184400 Ranks of (odd i)+(even j)*r, when all i+j*r are ranked; r=sqrt(2), i>=0, j>=0.

Original entry on oeis.org

2, 7, 9, 14, 18, 22, 24, 29, 35, 37, 41, 43, 50, 53, 58, 60, 65, 68, 72, 77, 80, 86, 89, 93, 95, 99, 103, 109, 113, 118, 120, 124, 128, 130, 135, 140, 145, 147, 152, 157, 159, 164, 169, 171, 175, 177, 183, 188, 190, 196, 202, 204, 208, 210, 216
Offset: 1

Views

Author

Clark Kimberling, Jan 12 2011

Keywords

Examples

			Writing (i,j) for i+j*r, the first 7 in the ranking are (0,0), (1,0), (0,1), (2,0), (1,1), (0,2), (3,0); the ranks where i is odd and j is even are 2,7.

Crossrefs

Cf. A184397, A184398, A184499, A184401, A184402, A184403.

A184401 Ranks of (even i)+(odd j)*r, when all i+j*r are ranked; r=sqrt(2), i>=0, j>=0.

Original entry on oeis.org

3, 8, 11, 16, 20, 25, 27, 32, 38, 40, 44, 47, 54, 57, 61, 64, 69, 73, 76, 81, 85, 90, 94, 98, 100, 104, 108, 114, 119, 123, 125, 129, 134, 136, 141, 146, 151, 153, 158, 163, 165, 170, 176, 178, 182, 184, 189, 195, 197, 203, 209, 211, 215
Offset: 1

Views

Author

Clark Kimberling, Jan 12 2011

Keywords

Examples

			Writing (i,j) for i+j*r, the first 7 in the ranking are (0,0), (1,0), (0,1), (2,0), (1,1), (0,2), (3,0); the rank where i is even and j is odd is 3.

Crossrefs

Cf. A184397, A184398, A184399, A184400, A184402, A184403.

A184402 Ranks of (even i)+(even j)*r, when all i+j*r are ranked; r=sqrt(2), i>=0, j>=0.

Original entry on oeis.org

1, 4, 6, 10, 13, 17, 19, 23, 28, 30, 34, 36, 42, 45, 49, 51, 56, 59, 62, 67, 70, 75, 78, 82, 84, 88, 91, 97, 101, 105, 107, 111, 115, 117, 122, 126, 131, 133, 138, 142, 144, 149, 154, 156, 160, 162, 167, 172, 174, 180, 185, 187, 191, 193, 199, 201, 205, 207
Offset: 1

Views

Author

Clark Kimberling, Jan 12 2011

Keywords

Examples

			Writing (i,j) for i+j*r, the first 7 in the ranking are (0,0), (1,0), (0,1), (2,0), (1,1), (0,2), (3,0); the ranks where i and j are both even are 1,4,6.

Crossrefs

Cf. A184397, A184398, A184399, A184400, A184401, A184403.

A184403 "Types" (parities of i and j) when all the numbers i+j*r are ranked, where r=sqrt(2), i>=0, j>=0.

Original entry on oeis.org

4, 2, 3, 4, 1, 4, 2, 3, 2, 4, 3, 1, 4, 2, 1, 3, 4, 2, 4, 3, 1, 2, 4, 2, 3, 1, 3, 4, 2, 4, 1, 3, 1, 4, 2, 4, 2, 3, 1, 3, 2, 4, 2, 3, 4, 1, 3, 1, 4, 2, 4, 1, 2, 3, 1, 4, 3, 2, 4, 2, 3, 4, 1, 3, 2, 1, 4, 2, 3, 4, 1, 2, 3, 1, 4, 3, 2, 4, 1, 2, 3, 4, 1, 4, 3, 2, 1, 4, 2, 3, 4, 1, 2, 3, 2, 1
Offset: 1

Views

Author

Clark Kimberling, Jan 12 2011

Keywords

Examples

			(See the examples at A184399-A184402.)

Crossrefs

Cf. A183993, A184338, A184397, A184398, A184399, A184400, A184401, A184402.

Formula

Let s(n)=i(n)+r*j(n) be the sequence obtained by arranging in increasing order all the numbers i+j*r, where
r=2^(1/2) and i>=0, j>=0. Then
a(n)=1 if i(n) is odd and j(n) is odd (n in A184399);
a(n)=2 if i(n) is odd and j(n) is even (n in A184400);
a(n)=3 if i(n) is even and j(n) is odd (n in A184401);
a(n)=4 if i(n) is even and j(n) is even (n in A184402).

A184399 Ranks of (odd i)+(odd j)*r, when all i+j*r are ranked; r=sqrt(2), i>=0, j>=0.

Original entry on oeis.org

5, 12, 15, 21, 26, 31, 33, 39, 46, 48, 52, 55, 63, 66, 71, 74, 79, 83, 87, 92, 96, 102, 106, 110, 112, 116, 121, 127, 132, 137, 139, 143, 148, 150, 155, 161, 166, 168, 173, 179, 181, 186, 192, 194, 198, 200, 206, 212, 214, 220, 227, 229, 233, 235, 241, 244, 248, 250, 257
Offset: 1

Views

Author

Clark Kimberling, Jan 12 2011

Keywords

Examples

			Writing (i,j) for i+j*r, the first 7 in the ranking are (0,0), (1,0), (0,1), (2,0), (1,1), (0,2), (3,0); the rank where i and j are both odd is 5.

Crossrefs

Cf. A184397, A184398, A184400, A184401, A184402, A184403.

A184410 Ranks of (odd i)+j/r when all i+j/r are ranked; r=sqrt(2), i>=0, j>=0. Complement of A184411.

Original entry on oeis.org

3, 5, 8, 11, 12, 15, 16, 20, 21, 25, 26, 27, 31, 32, 33, 38, 39, 40, 44, 46, 47, 48, 52, 54, 55, 57, 61, 63, 64, 66, 69, 71, 73, 74, 76, 79, 81, 83, 85, 87, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 119, 121, 123, 125, 127, 129
Offset: 1

Views

Author

Clark Kimberling, Jan 13 2011

Keywords

Examples

			Writing (i,j) for i+j/r, the first 7 in the ranking are (0,0), (0,1), (1,0), (0,2), (1,1), (2,0), (0,3); the ranks where i is odd are 3,5 and the ranks where i is even are 1,2,4,6,7.

Crossrefs

Cf. A184397, A184411, A184412, A184413, A184414, A184415, A184416.

A184411 Ranks of (even i)+j/r when all i+j/r are ranked; r=sqrt(2), i>=0, j>=0. Complement of A184410.

Original entry on oeis.org

1, 2, 4, 6, 7, 9, 10, 13, 14, 17, 18, 19, 22, 23, 24, 28, 29, 30, 34, 35, 36, 37, 41, 42, 43, 45, 49, 50, 51, 53, 56, 58, 59, 60, 62, 65, 67, 68, 70, 72, 75, 77, 78, 80, 82, 84, 86, 88, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 118, 120
Offset: 1

Views

Author

Clark Kimberling, Jan 13 2011

Keywords

Examples

			Writing (i,j) for i+j/r, the first 7 in the ranking are (0,0), (0,1), (1,0), (0,2), (1,1), (2,0), (0,3); the ranks where i is odd are 3,5 and the ranks where i is even are 1,2,4,6,7.

Crossrefs

Cf. A184397, A184410, A184412, A184413, A184414, A184415, A184416.
Showing 1-8 of 8 results.

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