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 1-5 of 5 results.

A115870 Terms at odd positions of A115869.

Original entry on oeis.org

0, 0, 0, 3, 0, 7, 5, 0, 0, 15, 13, 15, 9, 15, 13, 11, 0, 31, 29, 35, 25, 27, 0, 23, 17, 0, 45, 19, 25, 23, 21, 27, 0, 63, 61, 63, 57, 59, 61, 55, 49, 51, 61, 51, 57, 43, 53, 59, 33, 55, 45, 35, 41, 39, 37, 47, 49, 47, 45, 47, 41, 47, 45, 43, 0
Offset: 1

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Author

Antti Karttunen, Feb 07 2006

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Bisection of A115869.

A115857 Smallest integer m > n, such that there exists nonzero solutions to a cross-domain congruence n*i = m X i, n if no such integer exists.

Original entry on oeis.org

1, 2, 7, 4, 13, 14, 11, 8, 25, 26, 31, 28, 21, 22, 19, 16, 49, 50, 23, 52, 29, 62, 47, 56, 41, 42, 31, 44, 37, 38, 35, 32, 97, 98, 39, 100, 61, 46, 63, 104, 105, 58, 59, 124, 53, 94, 55, 112, 81, 82, 55, 84, 93, 62, 59, 88, 73, 74, 63, 76, 69, 70, 67, 64, 193, 194, 71, 196, 77
Offset: 1

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Author

Antti Karttunen, Feb 07 2006

Keywords

Comments

Here * stands for ordinary multiplication and X means carryless (GF(2)[X]) multiplication (A048720).

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a(2n) = 2*a(n). Bisection A115858 gives only the odd terms. Differs from A065621 for the first time at n=19, where a(19)=23, while A065621(19)=55. The next differences are a(21)=29 (A065621(21)=61) and a(23)=47 (A065621(23)=59). Cf. A115859, A115861, A115869, A115871, A115872.

A115871 Table listing for each n (in descending order) all m's <= n, such that there exists nonzero solutions to a cross-domain congruence m*i = n X i.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 3, 8, 9, 10, 11, 7, 12, 13, 5, 14, 6, 15, 16, 17, 18, 19, 15, 20, 21, 13, 22, 14, 23, 19, 15, 24, 25, 9, 26, 10, 27, 15, 28, 12, 29, 21, 13, 30, 31, 27, 11, 32, 33, 34, 35, 31, 36, 37, 29, 38, 30, 39, 35, 40, 41, 25, 42, 26, 43, 27, 44, 28, 45, 46, 38, 30, 47, 27
Offset: 1

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Author

Antti Karttunen, Feb 07 2006

Keywords

Comments

Here * stands for ordinary multiplication and X means carryless (GF(2)[X]) multiplication (A048720).

Examples

			Row n has A115861(n)+1 elements: 1; 2; 3; 4; 5; 6; 7,3; 8; 9; 10; 11,7; 12; 13,5; 14,6; 15; etc.

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Crossrefs

Cf. A115857, A115859, A115861, A115869, A115872.

A115859 Largest natural number m < n, such that there exists nonzero solutions to a cross-domain congruence m*i = n X i, zero if no such integer exists.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 7, 0, 5, 6, 0, 0, 0, 0, 15, 0, 13, 14, 19, 0, 9, 10, 15, 12, 21, 0, 27, 0, 0, 0, 31, 0, 29, 30, 35, 0, 25, 26, 27, 28, 0, 38, 27, 0, 17, 18, 0, 20, 45, 30, 51, 24, 25, 42, 55, 0, 45, 54, 59, 0, 0, 0, 63, 0, 61, 62, 67, 0, 57, 58, 71, 60, 69, 70, 63, 0
Offset: 1

Views

Author

Antti Karttunen, Feb 07 2006

Keywords

Comments

Here * stands for ordinary multiplication and X means carryless (GF(2)[X]) multiplication (A048720).

Links

Crossrefs

a(2n) = 2*a(n). Bisection A115860 gives the terms at odd positions. Differs from A115869 for the first time at n=23, where a(23)=19, while A115869(23)=15. Cf. A115857, A115861, A115871.

A115861 Number of distinct m's < n, such that there exists nonzero solutions to a cross-domain congruence m*i = n X i.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 1, 1, 2, 0, 2, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 2, 2, 0, 1, 1, 0, 1, 1, 1, 4, 1, 1, 2, 3, 0, 3, 2, 3, 0, 0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 2, 1, 3, 0, 1, 1, 2, 1, 1, 1, 2, 1, 2, 0, 4, 2, 2, 2, 2, 0, 1, 1, 4, 1, 2, 0
Offset: 1

Views

Author

Antti Karttunen, Feb 07 2006

Keywords

Links

Crossrefs

a(2n) = a(n). Cf. A115859, A115869, A115871.
Showing 1-5 of 5 results.

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