A260658 Numerators of a BBP-like formula for 4*Pi/sqrt(27).

5, -7, 23, -1, 41, -25, 59, -17, 77, -43, 95, -13, 113, -61, 131, -35, 149, -79, 167, -11, 185, -97, 203, -53, 221, -115, 239, -31, 257, -133, 275, -71, 293, -151, 311, -5, 329, -169, 347, -89, 365, -187, 383, -49, 401, -205, 419, -107, 437, -223, 455, -29, 473

Offset: 0

Author

David Brink, Nov 13 2015

Keywords

• sign
• frac

Comments

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

The reduced Collatz function R applied to the numbers 6n+3: a(n) = R(6n+3), where R(k) = (3k+1)/2^r, with r as large as possible, yields an unsigned version of this sequence. - Jonas Kaiser, Jun 17 2024

Links

• 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.

Crossrefs

Cf. A073010, A260659 (denominators).

Programs

Magma

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

Mathematica

A260658[n_] := Numerator[(-1/8)^n*(2/(3*n + 1) + 1/(3*n + 2))];
Array[A260658, 100, 0] (* Paolo Xausa, Jun 19 2024 *)

PARI

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

Formula

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

Extensions

More terms from Michel Marcus, Nov 15 2015