A208924 -id:A208924 - cp's OEIS frontend

A185064 Numbers k such that a Golay sequence of length k exists.

1, 2, 4, 8, 10, 16, 20, 26, 32, 40, 52, 64, 80, 100

Offset: 1

N. J. A. Sloane, Mar 02 2012

It is known that the sequence contains all numbers 2^i 10^j 26^m, and that all terms k > 1 are even and not divisible by any prime == 3 (mod 4). But the full characterization of these numbers is an open problem.

Dragomir Z. Dokovic, Equivalence classes and representatives of Golay sequences, Discrete Math. 189 (1998), no. 1-3, 79-93. MR1637705 (99j:94031).

Cf. A208924-A208929.

A208929 Let L = A185064(n) be the n-th length for which a Golay sequence exists; a(n) = number of equivalence classes of non-constructable Golay sequences of length L.

Original entry on oeis.org

1, 1, 0, 0, 2, 2, 1, 1, 44, 0

Offset: 1

N. J. A. Sloane, Mar 03 2012

Dragomir Z. Dokovic, Equivalence classes and representatives of Golay sequences, Discrete Math. 189 (1998), no. 1-3, 79-93. MR1637705 (99j:94031).

Cf. A185064, A208924-A208929.

A208927 Let L = A185064(n) be the n-th length for which a Golay sequence exists; a(n) = number of equivalence classes of Golay sequences of length L.

Original entry on oeis.org

1, 1, 1, 5, 2, 36, 25, 1, 336, 220

Offset: 1

N. J. A. Sloane, Mar 03 2012

Dragomir Z. Dokovic, Equivalence classes and representatives of Golay sequences, Discrete Math. 189 (1998), no. 1-3, 79-93. MR1637705 (99j:94031).

Cf. A185064, A208924-A208929. A208927=A208928+A208929.

A208928 Let L = A185064(n) be the n-th length for which a Golay sequence exists; a(n) = number of equivalence classes of constructable Golay sequences of length L.

Original entry on oeis.org

0, 0, 1, 5, 0, 34, 24, 0, 292, 220, 12, 3032, 2088, 128

Offset: 1

N. J. A. Sloane, Mar 03 2012

Dragomir Z. Dokovic, Equivalence classes and representatives of Golay sequences, Discrete Math. 189 (1998), no. 1-3, 79-93. MR1637705 (99j:94031).

Cf. A185064, A208924-A208929.

A208925 Let L = A185064(n) be the n-th length for which a Golay sequence exists; a(n) = number of constructable Golay sequences of length L.

Original entry on oeis.org

0, 0, 32, 192, 0, 1408, 1024, 0, 12544, 9728, 512, 132608, 94720, 8192

Offset: 1

N. J. A. Sloane, Mar 03 2012

The definition sounds paradoxical: how can a(n) possibly be zero? The answer seems to be that a Golay sequence of length L can exist without being "constructable"! - N. J. A. Sloane, Nov 26 2020

Dragomir Z. Dokovic, Equivalence classes and representatives of Golay sequences, Discrete Math. 189 (1998), no. 1-3, 79-93. MR1637705 (99j:94031).

Cf. A185064, A208924, A208926, A208927, A208928, A208929.

A208926 Let L = A185064(n) be the n-th length for which a Golay sequence exists; a(n) = number of non-constructable Golay sequences of length L.

Original entry on oeis.org

4, 8, 0, 0, 128, 128, 64, 64, 2816, 0, 0, 51712, 8192

Offset: 1

N. J. A. Sloane, Mar 03 2012

Dragomir Z. Dokovic, Equivalence classes and representatives of Golay sequences, Discrete Math. 189 (1998), no. 1-3, 79-93. MR1637705 (99j:94031).

Cf. A185064, A208924, A208925, A208927, A208928, A208929.

a(11)-a(13) from Vincenzo Librandi, Nov 26 2020

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A185064 Numbers k such that a Golay sequence of length k exists.

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A208929 Let L = A185064(n) be the n-th length for which a Golay sequence exists; a(n) = number of equivalence classes of non-constructable Golay sequences of length L.

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A208927 Let L = A185064(n) be the n-th length for which a Golay sequence exists; a(n) = number of equivalence classes of Golay sequences of length L.

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A208928 Let L = A185064(n) be the n-th length for which a Golay sequence exists; a(n) = number of equivalence classes of constructable Golay sequences of length L.

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A208925 Let L = A185064(n) be the n-th length for which a Golay sequence exists; a(n) = number of constructable Golay sequences of length L.

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A208926 Let L = A185064(n) be the n-th length for which a Golay sequence exists; a(n) = number of non-constructable Golay sequences of length L.

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