A233586 Coefficients of the generalized continued fraction expansion of twice the Euler constant, 2*gamma = a(1) +a(1)/(a(2) +a(2)/(a(3) +a(3)/(a(4) +a(4)/....))).

1, 6, 12, 19, 63, 263, 856, 2632, 7714, 9683, 888970, 1200867, 1691244, 2350415, 3433770, 4482812, 17544235, 48509602, 53801529, 114221223, 124712727, 997393454, 16681741997, 17954856574, 105651203040

Offset: 1

Author

Stanislav Sykora, Jan 06 2014

Keywords

• nonn

Comments

For more details on Blazys' expansions, see A233582.

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..670
• S. Sykora, Blazys' Expansions and Continued Fractions, Stans Library, Vol.IV, 2013, DOI 10.3247/sl4math13.001
• S. Sykora, PARI/GP scripts for Blazys expansions and fractions, OEIS Wiki

Crossrefs

Cf. A001620 (gamma).

Cf. Blazys' expansions: A233582 (Pi), A233583 (e), A233584 (sqrt(e)), A233585 (1/gamma), A233587 and Blazys' continued fractions: A233588, A233589, A233590, A233591.

Programs

Mathematica

BlazysExpansion[n_, mx_] := Block[{k = 1, x = n, lmt = mx + 1, s, lst = {}}, While[k < lmt, s = Floor[x]; x = 1/(x/s - 1); AppendTo[lst, s]; k++]; lst]; BlazysExpansion[2 EulerGamma, 29] (* Robert G. Wilson v, May 22 2014 *)

PARI

bx(x, nmax)={local(c, v, k); \\ Blazys expansion function
v = vector(nmax); c = x; for(k=1, nmax, v[k] = floor(c); c = v[k]/(c-v[k]); ); return (v); }
bx(2*Euler, 670) \\ Execution; use very high real precision

Formula

2*gamma = 1+1/(6+6/(12+12/(19+19/(63+63/(263+...))))).