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Position of first occurrence of n in the continued fraction for the Euler-Mascheroni constant (gamma).
2

%I #18 Jul 24 2013 13:37:25

%S 2,4,9,8,11,69,24,14,139,52,22,161,10,199,337,79,163,176,384,614,183,

%T 651,137,480,250,862,554,618,287,300,1952,166,150,2038,560,483,1284,

%U 681,306,20,349,1130,2280,1884,1903,2564,4753,717,31,2610,568,248,2171

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

%C 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 Weisstein, Sep 21 2011

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Euler-MascheroniConstantContinuedFraction.html">Euler-Mascheroni Constant Continued Fraction</a>

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

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

%Y Cf. A001620, A002852, A032523.

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

%K nonn,base

%O 1,1

%A _Eric W. Weisstein_

%E More terms from _Benoit Cloitre_, Oct 20 2002