A260658 -id:A260658 - cp's OEIS frontend

A260659 Denominators of a BBP-like formula for 4*Pi/sqrt(27).

2, 80, 3584, 1760, 745472, 4456448, 99614720, 265289728, 10905190400, 54492397568, 1065151889408, 1277752770560, 96619584290816, 450799767388160, 8321103999008768, 19017153114013696, 689613692941107200, 3102980143258271744, 55484347409204510720, 30822635849723674624

Offset: 0

David Brink, Nov 13 2015

4*Pi/sqrt(27) = Sum_{n >= 0} (-1/8)^n*(2/(3*n+1)+1/(3*n+2)).

Paolo Xausa, Table of n, a(n) for n = 0..1000
David H. Bailey, A Compendium of BBP-Type Formulas for Mathematical Constants.
David Brink, Nilakantha's accelerated series for pi, Acta Arith. 171 (2015), 293-308.

Cf. A073010, A260658 (numerators).

[Denominator((-1/8)^n*(2/(3*n+1)+1/(3*n+2))): n in [0..60]]; // Vincenzo Librandi, Nov 20 2015

A260659[n_] := Denominator[(-1/8)^n*(2/(3*n + 1) + 1/(3*n + 2))];
Array[A260659, 25, 0] (* Paolo Xausa, Jun 19 2024 *)

a(n) = denominator((-1/8)^n*(2/(3*n+1)+1/(3*n+2))); \\ Michel Marcus, Nov 15 2015

a(n) = denominator((-1/8)^n*(2/(3*n+1)+1/(3*n+2))).

More terms from Michel Marcus, Nov 15 2015

A373730 Reduced Collatz function R applied to the numbers 6n+1: a(n) = R(6n+1), where R(k) = (3k+1)/2^r, with r as large as possible.

Original entry on oeis.org

1, 11, 5, 29, 19, 47, 7, 65, 37, 83, 23, 101, 55, 119, 1, 137, 73, 155, 41, 173, 91, 191, 25, 209, 109, 227, 59, 245, 127, 263, 17, 281, 145, 299, 77, 317, 163, 335, 43, 353, 181, 371, 95, 389, 199, 407, 13, 425, 217, 443, 113, 461, 235, 479, 61, 497, 253, 515

Offset: 0

Jonas Kaiser, Jun 17 2024

Paolo Xausa, Table of n, a(n) for n = 0..10000

Cf. A000265, A017185, A075677, A260658.

A373730[n_] := #/2^IntegerExponent[#, 2] & [9*n + 2];
Array[A373730, 100, 0] (* Paolo Xausa, Aug 19 2024 *)

PARI
```
a(n) = n=9*n+2; n>>valuation(n,2);
```

a(n) = A000265(A017185(n)).

A373864 Reduced Collatz function R applied to the numbers 6n+5: a(n) = R(6n+5), where R(k) = (3k+1)/2^r, with r as large as possible.

Original entry on oeis.org

1, 17, 13, 35, 11, 53, 31, 71, 5, 89, 49, 107, 29, 125, 67, 143, 19, 161, 85, 179, 47, 197, 103, 215, 7, 233, 121, 251, 65, 269, 139, 287, 37, 305, 157, 323, 83, 341, 175, 359, 23, 377, 193, 395, 101, 413, 211, 431, 55, 449, 229, 467, 119

Offset: 0

Jonas Kaiser, Jun 19 2024

Paolo Xausa, Table of n, a(n) for n = 0..10000

Cf. A000265, A017257, A075677, A260658, A373730.

A373864[n_] := #/2^IntegerExponent[#, 2] & [9*n + 8];
Array[A373864, 100, 0] (* Paolo Xausa, Aug 19 2024 *)

PARI
```
a(n) = n=9*n+8; n>>valuation(n,2);
```

a(n) = A000265(A017257(n)).

cp's OEIS Frontend

A260659 Denominators of a BBP-like formula for 4*Pi/sqrt(27).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

Extensions

A373730 Reduced Collatz function R applied to the numbers 6n+1: a(n) = R(6n+1), where R(k) = (3k+1)/2^r, with r as large as possible.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A373864 Reduced Collatz function R applied to the numbers 6n+5: a(n) = R(6n+5), where R(k) = (3k+1)/2^r, with r as large as possible.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula