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 1-6 of 6 results.

A095359 Ratio A095109(n)/A095091(n) rounded down.

Original entry on oeis.org

0, 0, 0, 3, 6, 5, 12, 12, 20, 24, 42, 58, 97, 140, 286, 478, 841, 1504, 2788, 5048
Offset: 1

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Author

Antti Karttunen, Jun 12 2004

Keywords

Comments

This is the average diving index for those 4k+3 integers in range ]2^n,2^(n+1)] that "dive". See A095101.
The ratios before rounding are: 0, 0, 0, 3, 6.5, 5.714286, 12.933333, 12.548387, 20.691176, 24.635135, 42.903226, 58.98494, 97.742751, 140.742413, 286.896704, 478.786471, 841.487894, 1504.108692, 2788.84881, 5048.608416.

Crossrefs

A095360 gives the same ratios rounded to nearest integer. A095355 gives similar ratios computed only for 4k+3 primes.

Formula

a(n) = 0 if A095091(n) is 0, otherwise a(n) = floor(A095109(n)/A095091(n)).

A095360 Ratio A095109(n)/A095091(n) rounded to nearest integer.

Original entry on oeis.org

0, 0, 0, 3, 7, 6, 13, 13, 21, 25, 43, 59, 98, 141, 287, 479, 841, 1504, 2789, 5049
Offset: 1

Views

Author

Antti Karttunen, Jun 12 2004

Keywords

Crossrefs

See Comments on A095359, where the same ratios are given rounded down.

Formula

a(n) = 0 if A095091(n) is 0, otherwise a(n) = round(A095109(n)/A095091(n)).

A095110 Sum of maximal Motzkin path prefix-lengths of all 4k+3 integers in range ]2^n,2^(n+1)].

Original entry on oeis.org

2, 6, 24, 80, 303, 847, 3401, 12816, 47255, 168306, 628058, 2243714, 8741445, 33079519, 125266470, 474015314, 1806320048, 6945673364, 26539784794, 102630867522
Offset: 1

Views

Author

Antti Karttunen, Jun 01 2004

Keywords

Links

Crossrefs

Cf. A095270, A095109.

A095269 Diving index of 4n+3.

Original entry on oeis.org

0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 10, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 10, 0, 7, 0, 3, 0, 7, 7, 0, 0, 3, 0, 8, 0, 8, 0, 3, 0, 0, 0, 11, 0, 3, 0, 34, 0, 8, 19, 3, 0, 10, 13, 61, 0, 3, 0, 0, 7, 0, 0, 3, 0, 7, 0, 8, 0, 3, 0, 10, 0, 0, 0, 3, 0, 32, 0, 7, 0, 3, 0, 58, 0, 7, 0, 3, 0, 0
Offset: 0

Views

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

Cf. A004767, A095270, A095109, A095271 (same sequence with zeros removed).

Formula

a(n) = A095270(n)+1 modulo A004767(n).

A095106 Sum of diving indices of all 4k+3 primes in range ]2^n,2^(n+1)].

Original entry on oeis.org

0, 0, 0, 3, 3, 17, 94, 158, 213, 571, 1987, 3163, 27993, 45176, 205432, 707079, 2319521, 7603409, 25967812, 83981455, 310267532
Offset: 1

Views

Author

Antti Karttunen, Jun 01 2004

Keywords

Links

Crossrefs

Cf. A095104, A095107, A095109.

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

Views

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)).
Showing 1-6 of 6 results.

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