OFFSET
0,1
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.
FORMULA
a(n) = numerator((-1/8)^n*(2/(3*n+1)+1/(3*n+2))).
MATHEMATICA
A260658[n_] := Numerator[(-1/8)^n*(2/(3*n + 1) + 1/(3*n + 2))];
Array[A260658, 100, 0] (* Paolo Xausa, Jun 19 2024 *)
PROG
(PARI) a(n) = numerator((-1/8)^n*(2/(3*n+1) + 1/(3*n+2))); \\ Michel Marcus, Nov 15 2015
(Magma) [Numerator((-1/8)^n*(2/(3*n+1)+1/(3*n+2))): n in [0..60]]; // Vincenzo Librandi, Nov 20 2015
CROSSREFS
KEYWORD
sign,frac
AUTHOR
David Brink, Nov 13 2015
EXTENSIONS
More terms from Michel Marcus, Nov 15 2015
STATUS
approved