A233585 Coefficients of the generalized continued fraction expansion of the inverse of Euler constant, 1/gamma = a(1) +a(1)/(a(2) +a(2)/(a(3) +a(3)/(a(4) +a(4)/....))).

1, 1, 2, 2, 2, 2, 4, 12, 39, 71, 83, 484, 1028, 1447, 9913, 31542, 526880, 685669, 1396494, 1534902, 2295194, 9521643, 9643315, 42421746, 183962859, 553915624, 557976754, 6111180351, 10671513549, 61650520975, 106532505646

Offset: 1

Author

Stanislav Sykora, Jan 06 2014

Keywords

• nonn

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. A233582.

Cf. A001620 (gamma).

Cf. Blazys's expansions: A233582 (Pi), A233583(e), A233584 (sqrt(e)), A233586 (2*gamma), A233587 and Blazys's 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[1/EulerGamma, 35] (* Robert G. Wilson v, May 22 2014 *)
BlazysExpansion[n_, mx_] := Reap[Nest[(1/(#/Sow[Floor[#]] - 1)) &, n, mx];][[-1, 1]]; BlazysExpansion[1/EulerGamma, 35] (* Jan Mangaldan, Jan 04 2017 *)

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(1/Euler, 670) \\ Execution; use very high real precision

Formula

1/gamma = 1+1/(1+1/(2+2/(2+2/(2+2/(2+2/(4+4/(12+...))))))).