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.

A095361 Ratio A095110(n)/A000079(n-2) rounded down.

Original entry on oeis.org

2, 6, 12, 20, 37, 52, 106, 200, 369, 657, 1226, 2191, 4268, 8076, 15291, 28931, 55124, 105982, 202482, 391505
Offset: 1

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Author

Antti Karttunen, Jun 12 2004

Keywords

Comments

This is the average length of maximum Motzkin path prefix (i.e. non-diving portion) found in the "Jacobi-vectors" of all 4k+3 integers in range ]2^n,2^(n+1)]. See A095269-A095270.
The ratios before rounding are: 2, 6, 12, 20, 37.875, 52.9375, 106.28125, 200.25, 369.179687, 657.445312, 1226.675781, 2191.126953, 4268.283691, 8076.054443, 15291.317139, 28931.598755, 55124.513184, 105982.564758, 202482.488968, 391505.689705.

Crossrefs

A095362 gives the same ratios rounded to nearest integer. A095357 gives similar ratios computed only for 4k+3 primes.

Formula

a(1) = 2, a(n) = floor(A095110(n)/A000079(n-2)) for n > 1.

A095362 Ratio A095110(n)/A000079(n-2) rounded to nearest integer.

Original entry on oeis.org

2, 6, 12, 20, 38, 53, 106, 200, 369, 657, 1227, 2191, 4268, 8076, 15291, 28932, 55125, 105983, 202482, 391506
Offset: 1

Views

Author

Antti Karttunen, Jun 12 2004

Keywords

Crossrefs

See Comments on A095361, where the same ratios are given rounded down.
Cf. A000079, A095110.

Formula

a(1) = 2, a(n) = round(A095110(n)/A000079(n-2)) for n > 1.

A095109 Sum of diving indices of all 4k+3 integers in range ]2^n,2^(n+1)].

Original entry on oeis.org

0, 0, 0, 3, 13, 40, 194, 389, 1407, 3646, 13300, 39166, 131464, 389575, 1627565, 5556317, 19913811, 72249861, 272188855, 996509475
Offset: 1

Views

Author

Antti Karttunen, Jun 01 2004

Keywords

Comments

Diving index is explained at A095269.

Links

Crossrefs

Cf. A095110.

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.

A095270 Length of maximal Motzkin path prefix in the Jacobi-vector of 4n+3.

Original entry on oeis.org

2, 6, 10, 14, 2, 22, 26, 30, 34, 38, 2, 46, 9, 54, 58, 62, 2, 70, 74, 78, 82, 86, 2, 94, 9, 102, 6, 110, 2, 118, 6, 6, 130, 134, 2, 142, 7, 150, 7, 158, 2, 166, 170, 174, 10, 182, 2, 190, 33, 198, 7, 18, 2, 214, 9, 12, 60, 230, 2, 238, 242, 6, 250, 254, 2, 262
Offset: 1

Views

Author

Antti Karttunen, Jun 01 2004

Keywords

Links

Crossrefs

Cf. A004767, A095269, A095110, A095105.

Formula

a(n) = A095269(n)-1 modulo A004767(n).

A095357 Ratio A095107(n)/A095008(n) rounded down.

Original entry on oeis.org

2, 6, 10, 18, 35, 49, 108, 181, 346, 651, 1236, 2348, 4240, 8454, 16537, 30963, 60986, 118814, 225337, 438305, 854049
Offset: 1

Views

Author

Antti Karttunen, Jun 12 2004

Keywords

Comments

This is the average length of maximum Dyck path prefix (i.e. non-diving portion) found in the "Legendre-vectors" of all 4k+3 primes in range ]2^n,2^(n+1)]. See A095104-A095105.
The ratios before rounding are: 2, 6, 10, 18, 35.333333, 49.428571, 108.461538, 181.545455, 346.702703, 651.295775, 1236.34375, 2348.779221, 4240.445455, 8454.26518, 16537.703752, 30963.160864, 60986.990505, 118814.20247, 225337.874981, 438305.90522, 854049.74263.
Ratio (A095107(n)/A095008(n))/(A095110(n)/A000079(n-2)) starts as follows: 1, 1, 0.5, 0.75, 0.375, 0.4375, 0.40625, 0.34375, 0.289062, 0.277344, 0.25, 0.225586, 0.214844, 0.197021, 0.185425, 0.175293, 0.16391, 0.155701, 0.14756, 0.140224.

Crossrefs

A095358 gives the same ratios rounded to nearest integer. A095361 gives similar ratios computed for all 4k+3 integers.

Formula

a(n) = floor(A095107(n)/A095008(n)).
Showing 1-6 of 6 results.

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