A374188 -id:A374188 - cp's OEIS frontend

A374180 Numbers k such that K(3 / k) != K((-1)^floor(k/2)*k / 3), where K(a/b) is the Kronecker symbol. Row 1 of A374188.

2, 10, 26, 28, 34, 44, 50, 56, 58, 74, 76, 82, 88, 92, 98, 106, 112, 122, 124, 130, 140, 146, 152, 154, 170, 172, 176, 178, 184, 188, 194, 202, 218, 220, 224, 226, 236, 242, 248, 250, 266, 268, 274, 280, 284, 290, 298, 304, 314, 316, 322, 332, 338, 344, 346

Offset: 1

Peter Luschny, Jun 30 2024

nonn

Cf. A374188, A374181, A374182, A374183, A374184.

Cf. A372728 (Kronecker).

# see A374188
print(A374188_row(1, 350))

A374181 Numbers k such that K(7 / k) != K((-1)^floor(k/2)*k / 7), where K(a/b) is the Kronecker symbol. Row 2 of A374188.

Original entry on oeis.org

2, 10, 12, 18, 24, 26, 34, 44, 48, 50, 58, 60, 66, 74, 76, 82, 88, 90, 92, 96, 106, 108, 114, 120, 122, 124, 130, 138, 146, 152, 156, 162, 170, 172, 176, 178, 184, 186, 188, 192, 194, 202, 204, 216, 218, 220, 226, 234, 236, 240, 242, 248, 250, 258, 268, 274

Offset: 1

Peter Luschny, Jun 30 2024

nonn

Cf. A374188, A374180, A374182, A374183, A374184.

Cf. A372728 (Kronecker).

# see A374188
print(A374188_row(2, 350))

A374182 Numbers k such that K(11 / k) != K((-1)^floor(k/2)*k / 11), where K(a/b) is the Kronecker symbol. Row 3 of A374188.

Original entry on oeis.org

2, 10, 12, 18, 24, 26, 28, 34, 42, 48, 50, 56, 58, 60, 74, 76, 82, 90, 92, 96, 98, 106, 108, 112, 114, 120, 122, 124, 130, 138, 140, 146, 152, 156, 162, 170, 172, 178, 184, 186, 188, 192, 194, 202, 204, 210, 216, 218, 224, 226, 234, 236, 240, 248, 250, 252

Offset: 1

Peter Luschny, Jun 30 2024

nonn

Cf. A374188, A374180, A374181, A374183, A374184.

Cf. A372728 (Kronecker).

# see A374188
print(A374188_row(3, 350))

A374183 Numbers k such that K(15 / k) != K((-1)^floor(k/2)*k / 15), where K(a/b) is the Kronecker symbol. Row 4 of A374188.

Original entry on oeis.org

2, 26, 28, 34, 44, 56, 58, 74, 76, 82, 88, 92, 98, 106, 112, 122, 124, 146, 152, 154, 172, 176, 178, 184, 188, 194, 202, 218, 224, 226, 236, 242, 248, 266, 268, 274, 284, 298, 304, 314, 316, 322, 332, 338, 344, 346, 352, 362, 364, 368, 376, 386, 394, 412, 418

Offset: 1

Peter Luschny, Jun 30 2024

nonn

Cf. A374188, A374180, A374181, A374182, A374184.

Cf. A372728 (Kronecker).

# see A374188
print(A374188_row(4, 350))

A374184 Numbers k such that K(19 / k) != K((-1)^floor(k/2)*k / 19), where K(a/b) is the Kronecker symbol. Row 5 of A374188.

Original entry on oeis.org

2, 10, 12, 18, 24, 26, 28, 34, 42, 44, 48, 50, 56, 58, 60, 66, 74, 82, 88, 90, 92, 96, 98, 106, 108, 112, 120, 122, 124, 130, 138, 140, 146, 154, 156, 162, 170, 172, 176, 178, 184, 186, 188, 192, 194, 202, 204, 210, 216, 218, 220, 224, 226, 234, 236, 240, 242

Offset: 1

Peter Luschny, Jun 30 2024

nonn

Cf. A374188, A374180, A374181, A374182, A374183.

Cf. A372728 (Kronecker).

# see A374188
print(A374188_row(5, 350))

A374189 The values of A374188, seen as an ordered set.

Original entry on oeis.org

2, 10, 12, 18, 24, 26, 28, 34, 42, 44, 48, 50, 56, 58, 60, 66, 74, 76, 82, 88, 90, 92, 96, 98, 106, 108, 112, 114, 120, 122, 124, 130, 138, 140, 146, 152, 154, 156, 162, 170, 172, 176, 178, 184, 186, 188, 192, 194, 202, 204, 210, 216, 218, 220, 224, 226, 234, 236, 240

Offset: 1

Peter Luschny, Jul 01 2024

nonn

k is a term if and only if there exists a positive integer a of the form 4*n - 1, such that K(a / k) != K((-1)^floor(k/2)*k / a), where K denotes the Kronecker symbol (A372728).

			34 is a term, because K(15/34) = 1, but K(-34/15) = -1.
18 is a term, because K(19/18) = 1, but K(-18/19) = -1.

Cf. A374188, A372728, A374157.

All terms are even.

A374187 Least a of the form 4n - 1 (n>=1) such that there is a positive integer k so that K(a / k) != K((-1)^floor(k/2)k / a), where K denotes the Kronecker symbol (A372728).

Original entry on oeis.org

3, 3, 7, 7, 7, 3, 3, 3, 11, 3, 7, 3, 3, 3, 7, 7, 3, 3, 3, 3, 7, 3, 7, 3, 3, 7, 3, 7, 7, 3, 3, 3, 7, 3, 3, 3, 3, 7, 7, 3, 3, 3, 3, 3, 7, 3, 7, 3, 3, 7, 11, 7, 3, 3, 3, 3, 7, 3, 7, 3, 3, 3, 11, 7, 3, 3, 3, 3, 7, 3, 3, 3, 7, 3, 7, 7, 3, 3, 3, 7, 3, 3, 3, 3, 7, 3

Offset: 1

Peter Luschny, Jul 02 2024

nonn

These values witness the correctness of A374189. They seem to grow very slowly.

Cf. A374189, A374188, A372728.

cp's OEIS Frontend

A374180 Numbers k such that K(3 / k) != K((-1)^floor(k/2)*k / 3), where K(a/b) is the Kronecker symbol. Row 1 of A374188.

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A374181 Numbers k such that K(7 / k) != K((-1)^floor(k/2)*k / 7), where K(a/b) is the Kronecker symbol. Row 2 of A374188.

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A374182 Numbers k such that K(11 / k) != K((-1)^floor(k/2)*k / 11), where K(a/b) is the Kronecker symbol. Row 3 of A374188.

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SageMath

A374183 Numbers k such that K(15 / k) != K((-1)^floor(k/2)*k / 15), where K(a/b) is the Kronecker symbol. Row 4 of A374188.

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Programs

SageMath

A374184 Numbers k such that K(19 / k) != K((-1)^floor(k/2)*k / 19), where K(a/b) is the Kronecker symbol. Row 5 of A374188.

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SageMath

A374189 The values of A374188, seen as an ordered set.

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A374187 Least a of the form 4*n - 1 (n>=1) such that there is a positive integer k so that K(a / k) != K((-1)^floor(k/2)*k / a), where K denotes the Kronecker symbol (A372728).

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Crossrefs

A374187 Least a of the form 4n - 1 (n>=1) such that there is a positive integer k so that K(a / k) != K((-1)^floor(k/2)k / a), where K denotes the Kronecker symbol (A372728).