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 1-4 of 4 results.

A095355 Ratio A095106(n)/A095093(n) rounded down.

Original entry on oeis.org

0, 0, 0, 3, 3, 5, 15, 13, 10, 13, 25, 22, 97, 85, 203, 359, 625, 1067, 1880, 3166, 6068
Offset: 1

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Author

Antti Karttunen, Jun 12 2004

Keywords

Comments

This is the average diving index for those 4k+3 primes in range ]2^n,2^(n+1)] that "dive". See A095103.
The ratios before rounding are: 0, 0, 0, 3, 3, 5.666667, 15.666667, 13.166667, 10.142857, 13.926829, 25.805195, 22.118881, 97.536585, 85.237736, 203.39802, 359.470768, 625.039342, 1067.145123, 1880.907721, 3166.124599, 6068.683879.
Ratio (A095106(n)/A095093(n))/(A095109(n)/A095091(n)) starts as follows: 0, 0, 0, 1, 0.5, 0.428571, 0.4, 0.387097, 0.308824, 0.277027, 0.248387, 0.215361, 0.213383, 0.191474, 0.178036, 0.169496, 0.156814, 0.148329, 0.141456, 0.134383.

Crossrefs

A095356 gives the same ratios rounded to nearest integer. A095359 gives similar ratios computed for all 4k+3 integers.

Formula

a(n) = 0 if A095093(n) is 0, otherwise a(n) = floor(A095106(n)/A095093(n)).

A095356 Ratio A095106(n)/A095093(n) rounded to nearest integer.

Original entry on oeis.org

0, 0, 0, 3, 3, 6, 16, 13, 10, 14, 26, 22, 98, 85, 203, 359, 625, 1067, 1881, 3166, 6069
Offset: 1

Views

Author

Antti Karttunen, Jun 12 2004

Keywords

Crossrefs

Cf. A095355, where the same ratios are given round down.

Formula

a(n) = 0 if A095093(n) is 0, otherwise a(n) = round(A095106(n)/A095093(n)).

A095104 Diving index of the n-th 4k+3 prime (A002145(n)).

Original entry on oeis.org

0, 0, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 7, 7, 0, 3, 0, 3, 0, 11, 0, 0, 3, 13, 61, 0, 0, 0, 0, 3, 3, 0, 3, 7, 0, 45, 3, 0, 0, 0, 0, 7, 7, 35, 0, 7, 35, 3, 0, 3, 3, 0, 3, 15, 0, 0, 3, 15, 3, 0, 0, 7, 3, 0, 45, 3, 0, 0, 3, 3, 7, 7, 0, 3, 0, 3, 0, 3, 0, 0, 7, 7, 0, 0, 0, 67, 0, 0, 3, 0
Offset: 1

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Author

Antti Karttunen, Jun 01 2004

Keywords

Comments

Diving index of an odd number n is the first integer u > 1 where Sum_{i=1..u} J(i/n) results -1 and zero if never. Here J(i/n) is Jacobi symbol of i and n, which reduces to a Legendre symbol L(i/n) when n is a prime.

Links

Crossrefs

a(n)=A095105(n)+1 modulo A002145(n). Cf. A095106, A095108 (same sequence with zeros removed), A095269.

A095107 Sum of maximal Dyck path prefix lengths of all 4k+3 primes in range ]2^n,2^(n+1)].

Original entry on oeis.org

2, 6, 10, 54, 106, 346, 1410, 3994, 12828, 46242, 158252, 542568, 1865796, 6822592, 25120772, 88926198, 327561126, 1212380122, 4358259840, 16111686770, 59936356888
Offset: 1

Views

Author

Antti Karttunen, Jun 01 2004

Keywords

Links

Crossrefs

Cf. A095105, A095106, A095110.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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