A033149 Position of first occurrence of n in the continued fraction for the Euler-Mascheroni constant (gamma).

2, 4, 9, 8, 11, 69, 24, 14, 139, 52, 22, 161, 10, 199, 337, 79, 163, 176, 384, 614, 183, 651, 137, 480, 250, 862, 554, 618, 287, 300, 1952, 166, 150, 2038, 560, 483, 1284, 681, 306, 20, 349, 1130, 2280, 1884, 1903, 2564, 4753, 717, 31, 2610, 568, 248, 2171

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• base

Comments

The smallest positive integers not appearing in the first 970,258,158 terms of the c.f. are 13161, 13295, 14734, 14970, 14971, 15795, 15985, 16011, 16110, ... - Eric W. Weisstein, Sep 21 2011

Links

• Eric Weisstein's World of Mathematics, Euler-Mascheroni Constant Continued Fraction

Crossrefs

Cf. A001620, A002852, A032523.

Cf. A224847 (= a(n) -1).

Programs

Mathematica

With[{cf=ContinuedFraction[EulerGamma,5000]},Table[Position[cf,n,1,1],{n,60}]]//Flatten (* Harvey P. Dale, Aug 06 2025 *)

PARI

/* 15000 precision digits */ v=contfrac(Euler); a(n)=if(n<0,0,s=1; while(abs(n-component(v,s))>0,s++); s)

Formula

a(n) = A224847(n) + 1.

Extensions

More terms from Benoit Cloitre, Oct 20 2002