A257332 -id:A257332 - cp's OEIS frontend

A257347 1 followed by the numbers successively added to the four arms of the spirals in A257329, A257330, A257331, A257332.

1, 2, 3, 5, 7, 11, 4, 6, 9, 13, 17, 19, 23, 25, 29, 8, 15, 21, 31, 35, 14, 37, 41, 43, 47, 27, 49, 16, 12, 10, 33, 53, 59, 39, 61, 67, 22, 20, 18, 45, 65, 71, 73, 79, 83, 24, 51, 55, 26, 85, 77, 89, 97, 32, 57, 91, 101, 95, 28, 69, 103, 107

Offset: 1

N. J. A. Sloane, Apr 30 2015

nonn

Conjectured to be a permutation of the natural numbers.

Popular Computing (Calabasas, CA), Problem 146: Gcd, Vol. 4 (No. 45, Dec 1976), page PC45-4.
N. J. A. Sloane, Spirals showing initial terms of A257321-A257332

Cf. A257329, A257330, A257331, A257332.

A257321 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "2" arm.

Original entry on oeis.org

2, 5, 7, 5, 3, 11, 5, 2, 7, 2, 3, 2, 5, 2, 5, 7, 3, 5, 7, 2, 5, 7, 11, 3, 7, 3, 5, 3, 5, 3, 5, 3, 7, 3, 2, 5, 2, 7, 2, 3, 5, 7, 2, 7, 2, 7, 2, 7, 2, 5, 11, 2, 5, 2, 3, 2, 5, 2, 5, 7, 3, 7, 3, 7, 3, 5, 3, 5, 3, 5, 7, 2, 5, 7, 3, 7, 3, 7, 3, 2, 5, 2, 7, 2, 3, 5

Offset: 1

N. J. A. Sloane, Apr 21 2015

nonn

Place numbers 2,3,5,7 clockwise around a grid point (see illustrations in links). Divide grid into four spiral arms.
Extend each arm one step at a time, in rotation: first the 2 arm, then the 3 arm, then the 5 arm,  then the 7 arm, then the 2 arm, etc.
Rule for extending: next term in arm is smallest number such that each cell in the grid is relatively prime to its eight neighbors.
Repetitions in arms are permitted.
The four arms are A257321, A257322, A257323, A257324.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Popular Computing (Calabasas, CA), Problem 146: Gcd, Vol. 4 (No. 45, Dec 1976), page PC45-4.
N. J. A. Sloane, Spirals showing initial terms of A257321-A257332

Cf. A064413, A257322-A257340.

More terms from Lars Blomberg, Apr 27 2015

A257329 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "2" arm.

Original entry on oeis.org

2, 11, 13, 25, 21, 37, 27, 10, 39, 20, 71, 24, 85, 32, 95, 107, 115, 121, 125, 46, 145, 151, 155, 99, 167, 105, 181, 117, 197, 205, 211, 141, 223, 147, 76, 159, 86, 263, 72, 259, 135, 289, 30, 311, 60, 301, 94, 337, 116, 341, 343, 110, 359, 112, 237, 122, 389

Offset: 1

N. J. A. Sloane, Apr 21 2015

nonn

Place numbers 2,3,5,7 clockwise around a grid point (see illustrations in links). Divide grid into four spiral arms.
Extend each arm one step at a time, in rotation: first the 2 arm, then the 3 arm, then the 5 arm, then the 7 arm, then the 2 arm, etc.
Rule for extending: next term in arm is smallest number such that each cell in the grid is relatively prime to its eight neighbors. Every term in the entire grid must be different.
The four arms are A257329, A257330, A257331, A257332.
Conjecture: every number > 1 appears in one of the four arms.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Popular Computing (Calabasas, CA), Problem 146: Gcd, Vol. 4 (No. 45, Dec 1976), page PC45-4.
N. J. A. Sloane, Spirals showing initial terms of A257321-A257332

Cf. A064413, A257321-A257340, A257347 (the union list).

More terms from Lars Blomberg, Apr 27 2015

A257330 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "3" arm.

Original entry on oeis.org

3, 4, 17, 29, 31, 41, 49, 33, 61, 18, 73, 51, 77, 57, 28, 109, 34, 127, 38, 87, 62, 157, 40, 163, 169, 175, 187, 193, 64, 209, 203, 221, 227, 239, 153, 245, 171, 269, 177, 281, 293, 299, 189, 313, 201, 106, 207, 70, 219, 100, 347, 84, 361, 96, 379, 243, 391

Offset: 1

N. J. A. Sloane, Apr 21 2015

nonn

Place numbers 2,3,5,7 clockwise around a grid point (see illustrations in links). Divide grid into four spiral arms.
Extend each arm one step at a time, in rotation: first the 2 arm, then the 3 arm, then the 5 arm, then the 7 arm, then the 2 arm, etc.
Rule for extending: next term in arm is smallest number such that each cell in the grid is relatively prime to its eight neighbors. Every term in the entire grid must be different.
The four arms are A257329, A257330, A257331, A257332.
Conjecture: every number > 1 appears in one of the four arms.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Popular Computing (Calabasas, CA), Problem 146: Gcd, Vol. 4 (No. 45, Dec 1976), page PC45-4.
N. J. A. Sloane, Spirals showing initial terms of A257321-A257332

Cf. A064413, A257321-A257340, A257347 (the union list).

More terms from Lars Blomberg, Apr 27 2015

A257331 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "5" arm.

Original entry on oeis.org

5, 6, 19, 8, 35, 43, 16, 53, 67, 45, 79, 55, 89, 91, 69, 113, 36, 131, 63, 139, 75, 44, 111, 50, 173, 52, 185, 58, 123, 68, 215, 74, 229, 235, 241, 251, 253, 265, 277, 275, 287, 80, 307, 295, 317, 165, 331, 213, 323, 78, 349, 195, 367, 225, 371, 365, 397, 249

Offset: 1

N. J. A. Sloane, Apr 21 2015

nonn

Place numbers 2,3,5,7 clockwise around a grid point (see illustrations in links). Divide grid into four spiral arms.
Extend each arm one step at a time, in rotation: first the 2 arm, then the 3 arm, then the 5 arm, then the 7 arm, then the 2 arm, etc.
Rule for extending: next term in arm is smallest number such that each cell in the grid is relatively prime to its eight neighbors. Every term in the entire grid must be different.
The four arms are A257329, A257330, A257331, A257332.
Conjecture: every number > 1 appears in one of the four arms.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Popular Computing (Calabasas, CA), Problem 146: Gcd, Vol. 4 (No. 45, Dec 1976), page PC45-4.
N. J. A. Sloane, Spirals showing initial terms of A257321-A257332

Cf. A064413, A257321-A257340, A257347 (the union list).

More terms from Lars Blomberg, Apr 27 2015

A257322 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "3" arm.

Original entry on oeis.org

3, 2, 7, 3, 5, 7, 3, 7, 3, 2, 11, 3, 11, 3, 2, 5, 2, 7, 2, 7, 2, 11, 2, 5, 7, 3, 5, 7, 2, 11, 3, 5, 3, 5, 3, 5, 3, 7, 3, 7, 5, 7, 3, 7, 3, 2, 5, 2, 5, 2, 7, 2, 7, 2, 3, 11, 3, 2, 5, 2, 5, 2, 5, 7, 3, 5, 7, 2, 7, 2, 7, 2, 7, 2, 5, 11, 7, 3, 7, 3, 7, 3, 5, 3, 5

Offset: 1

N. J. A. Sloane, Apr 21 2015

nonn

Place numbers 2,3,5,7 clockwise around a grid point (see illustrations in links). Divide grid into four spiral arms.
Extend each arm one step at a time, in rotation: first the 2 arm, then the 3 arm, then the 5 arm, then the 7 arm, then the 2 arm, etc.
Rule for extending: next term in arm is smallest number such that each cell in the grid is relatively prime to its eight neighbors.
Repetitions in arms are permitted.
The four arms are A257321, A257322, A257323, A257324.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Popular Computing (Calabasas, CA), Problem 146: Gcd, Vol. 4 (No. 45, Dec 1976), page PC45-4.
N. J. A. Sloane, Spirals showing initial terms of A257321-A257332

Cf. A064413, A257321-A257340.

More terms from Lars Blomberg, Apr 27 2015

A257323 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "5" arm.

Original entry on oeis.org

5, 2, 11, 2, 5, 7, 2, 5, 7, 3, 5, 3, 5, 3, 7, 3, 2, 11, 3, 5, 7, 2, 7, 2, 7, 2, 5, 2, 3, 2, 5, 2, 5, 7, 3, 7, 3, 5, 3, 5, 7, 2, 5, 7, 3, 7, 3, 7, 3, 2, 11, 3, 5, 3, 5, 3, 5, 3, 7, 3, 2, 5, 2, 5, 2, 7, 2, 7, 2, 3, 5, 7, 2, 7, 2, 7, 2, 7, 2, 5, 7, 3, 5, 11, 2, 5

Offset: 1

N. J. A. Sloane, Apr 21 2015

nonn

Place numbers 2,3,5,7 clockwise around a grid point (see illustrations in links). Divide grid into four spiral arms.
Extend each arm one step at a time, in rotation: first the 2 arm, then the 3 arm, then the 5 arm, then the 7 arm, then the 2 arm, etc.
Rule for extending: next term in arm is smallest number such that each cell in the grid is relatively prime to its eight neighbors.
Repetitions in arms are permitted.
The four arms are A257321, A257322, A257323, A257324.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Popular Computing (Calabasas, CA), Problem 146: Gcd, Vol. 4 (No. 45, Dec 1976), page PC45-4.
N. J. A. Sloane, Spirals showing initial terms of A257321-A257332

Cf. A064413, A257321-A257340.

More terms from Lars Blomberg, Apr 27 2015

A257324 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "7" arm.

Original entry on oeis.org

7, 3, 11, 3, 2, 11, 2, 11, 2, 5, 7, 2, 3, 11, 3, 5, 3, 7, 5, 7, 3, 7, 3, 2, 5, 2, 7, 2, 3, 11, 3, 2, 5, 2, 5, 2, 5, 7, 2, 7, 2, 7, 2, 11, 2, 5, 7, 3, 7, 3, 5, 3, 5, 7, 2, 3, 5, 3, 5, 3, 5, 3, 11, 3, 2, 7, 3, 7, 3, 7, 5, 7, 3, 7, 3, 2, 5, 2, 5, 2, 5, 2, 7, 2, 7

Offset: 1

N. J. A. Sloane, Apr 21 2015

nonn

Place numbers 2,3,5,7 clockwise around a grid point (see illustrations in links). Divide grid into four spiral arms.
Extend each arm one step at a time, in rotation: first the 2 arm, then the 3 arm, then the 5 arm, then the 7 arm, then the 2 arm, etc.
Rule for extending: next term in arm is smallest number such that each cell in the grid is relatively prime to its eight neighbors.
Repetitions in arms are permitted.
The four arms are A257321, A257322, A257323, A257324.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Popular Computing (Calabasas, CA), Problem 146: Gcd, Vol. 4 (No. 45, Dec 1976), page PC45-4.
N. J. A. Sloane, Spirals showing initial terms of A257321-A257332

Cf. A064413, A257321-A257340.

More terms from Lars Blomberg, Apr 27 2015

A257325 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "2" arm.

Original entry on oeis.org

2, 5, 7, 11, 3, 13, 17, 4, 19, 6, 23, 8, 29, 14, 9, 25, 21, 31, 15, 16, 37, 41, 27, 43, 33, 47, 49, 39, 53, 45, 59, 35, 51, 61, 10, 67, 20, 71, 26, 57, 73, 79, 32, 65, 12, 55, 18, 77, 24, 83, 89, 34, 69, 38, 85, 22, 95, 28, 75, 91, 81, 97, 87, 101, 63, 103, 93

Offset: 1

N. J. A. Sloane, Apr 21 2015

nonn

Place numbers 2,3,5,7 clockwise around a grid point (see illustrations in links). Divide grid into four spiral arms.
Extend each arm one step at a time, in rotation: first the 2 arm, then the 3 arm, then the 5 arm, then the 7 arm, then the 2 arm, etc.
Rule for extending: next term in arm is smallest number such that each cell in the grid is relatively prime to its eight neighbors. Inside an arm, the terms must be distinct.
Repetitions between arms are permitted.
The four arms are A257325, A257326, A257327, A257328.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Popular Computing (Calabasas, CA), Problem 146: Gcd, Vol. 4 (No. 45, Dec 1976), page PC45-4.
N. J. A. Sloane, Spirals showing initial terms of A257321-A257332

Cf. A064413, A257321-A257340.

More terms from Lars Blomberg, Apr 27 2015

A257326 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "3" arm.

Original entry on oeis.org

3, 2, 7, 9, 5, 13, 15, 17, 11, 4, 19, 23, 21, 25, 8, 29, 10, 31, 14, 37, 16, 41, 22, 43, 47, 27, 53, 55, 26, 35, 33, 49, 59, 61, 67, 71, 65, 73, 77, 79, 83, 39, 89, 97, 101, 32, 103, 20, 91, 34, 107, 40, 109, 38, 51, 113, 57, 28, 85, 44, 119, 46, 81, 121, 45

Offset: 1

N. J. A. Sloane, Apr 21 2015

nonn

Place numbers 2,3,5,7 clockwise around a grid point (see illustrations in links). Divide grid into four spiral arms.
Extend each arm one step at a time, in rotation: first the 2 arm, then the 3 arm, then the 5 arm, then the 7 arm, then the 2 arm, etc.
Rule for extending: next term in arm is smallest number such that each cell in the grid is relatively prime to its eight neighbors. Inside an arm, the terms must be distinct.
Repetitions between arms are permitted.
The four arms are A257325, A257326, A257327, A257328.

Lars Blomberg, Table of n, a(n) for n = 1..10000
Popular Computing (Calabasas, CA), Problem 146: Gcd, Vol. 4 (No. 45, Dec 1976), page PC45-4.
N. J. A. Sloane, Spirals showing initial terms of A257321-A257332

Cf. A064413, A257321-A257340.

More terms from Lars Blomberg, Apr 27 2015

cp's OEIS Frontend

A257347 1 followed by the numbers successively added to the four arms of the spirals in A257329, A257330, A257331, A257332.

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A257321 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "2" arm.

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A257329 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "2" arm.

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A257330 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "3" arm.

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A257331 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "5" arm.

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A257322 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "3" arm.

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A257323 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "5" arm.

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A257324 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "7" arm.

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A257325 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "2" arm.

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A257326 Construct spiral of numbers on square grid as in Comments; sequence gives terms along the "3" arm.

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Author

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