A381083 -id:A381083 - cp's OEIS frontend

A381085 Column k=2 of Brent's table A381083 related to prime gaps 2n.

0, 0, 2, 4, 6, 56, 40, 40, 92, 624, 504, 10880, 6688, 7400, 19312, 113792, 122400, 3979008, 2239104, 2915840, 5777920, 56689920, 55372800, 110218240, 78453760, 65815552, 125480960, 2057036800, 1776107520, 137449159680, 56911196160, 54069370880, 127085826560, 63757824000, 96876953600, 4341200912384, 2258481971200, 2411472967680, 5056905641984, 122267833425920

Offset: 1

R. J. Mathar, Feb 13 2025

nonn

R. J. Mathar, Table of n, a(n) for n = 1..717
Richard P. Brent, Tables of T[r,k] and A[r,k], (1970) [unpublished].
Richard P. Brent, The distribution of small gaps between successive primes, Mathematics of Computation 28 (1974), 315-324. JSTOR 2005842

Cf. A381083 (irreg. triangle), A381084 (k=1), A381086 (k=3).

Maple
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See A381083.
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a(n) = A381083(n,2).

A381084 Column k=1 of Brent's table A381083 related to prime gaps 2n.

Original entry on oeis.org

1, 1, 2, 3, 4, 30, 18, 15, 30, 180, 150, 2970, 1620, 1782, 3960, 22275, 23760, 757350, 400950, 504900, 908820, 8835750, 8330850, 15904350, 10602900, 8675100, 15904350, 257650470, 222660900, 16604141400, 6441261750, 6226553025, 13836784500, 6641656560, 9962484840, 435858711750, 224155908900, 230748729750, 475482231000, 11332326505500, 8717174235000

Offset: 1

R. J. Mathar, Feb 13 2025

nonn

R. J. Mathar, Table of n, a(n) for n = 1..731
Richard P. Brent, Tables of T[r,k] and A[r,k], (1970) [unpublished].
Richard P. Brent, The distribution of small gaps between successive primes, Mathematics of Computation 28 (1974), 315-324. JSTOR 2005842

Cf. A381083 (irreg. triangle), A381085 (k=2), A381086 (k=3)

Maple
```
See A381083.
```

a(n) = A381083(n,1).

A381086 Column k=3 of Brent's table A381083 related to prime gaps 2n.

Original entry on oeis.org

0, 0, 0, 1, 2, 30, 28, 36, 100, 812, 632, 15642, 11090, 12312, 38958, 244829, 265734, 8883060, 5333232, 7236810, 16006998, 159615504, 161805900, 337714368, 259208326, 222480280, 445109722, 7401008550, 6375729282, 514590231096, 228830896980, 213249174660, 532897145178, 280475561070, 432135635850, 19890493216704, 10485155702790, 11646227156256, 24879391641270

Offset: 1

R. J. Mathar, Feb 13 2025

nonn

R. J. Mathar, Table of n, a(n) for n = 1..209
Richard P. Brent, Tables of T[r,k] and A[r,k], (1970) [unpublished].
Richard P. Brent, The distribution of small gaps between successive primes, Mathematics of Computation 28 (1974), 315-324. JSTOR 2005842

Cf. A381083 (irreg. triangle), A381084 (k=1), A381085 (k=2).

Maple
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See A381083.
```

a(n) = A381083(n,3).

A380948 Denominators of rational coefficients which are ratio of Brent's coefficients -A[n,2]/A343480.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 2, 2, 4, 8, 16, 2, 40, 32, 80, 20, 112, 1120, 320, 112, 112, 640, 32, 1120, 160, 5600, 280, 64, 1820, 116480, 2240, 14560, 232960, 3136, 364, 18200, 34, 116480, 618800, 76160, 10640, 1074944, 30464, 110656, 18811520, 13600, 2434432, 181060880, 15232, 3043040

Offset: 1

Artur Jasinski, Feb 09 2025

Brent's coefficients -A[n,2]/A343480 are rationals =  A380947(n)/ A380948(n).
Brent's coefficients are used in formulas of number of primes with particular distance to next prime =2*n.
Brent's coefficients A[n,1]/A114907 = B[n,1]/A114907 are equal to A380839(n)/A307410(n).

R. P. Brent, The distribution of small gaps between successive primes, Mathematics of Computation 28 (1974), 315-324.

Cf. A307410, A380839, A343480, A380947, A381083.

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A381085 Column k=2 of Brent's table A381083 related to prime gaps 2n.

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A381084 Column k=1 of Brent's table A381083 related to prime gaps 2n.

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A381086 Column k=3 of Brent's table A381083 related to prime gaps 2n.

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A380948 Denominators of rational coefficients which are ratio of Brent's coefficients -A[n,2]/A343480.

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