A248660 - OEIS

%I #37 Feb 16 2025 08:33:23

%S 0,5,3,10,1,1,4,1,1,1,1,9,1,1,12,2,17,2,2,1,1,17,1,6,4,1,3,3,4,2,1,

%T 262,2,1,4,1,49,2,1,9,1,2,1,1,4,23,26,6,6,5,3,3,1,1,1,144,9,1,1,5,1,3,

%U 1,1,5,13,8619,2,1,45,2,1,1,2,1,4,5,1,7,2,2,2,1,1,2,1,1,2,2,6,3,1,1,2,2,7,3,136,1

%N Simple continued fraction expansion of the constant defined in A037077.

%C A037077 is sometimes called the MRB constant.

%D Steven R. Finch, Mathematical Constants, Cambridge, 2003, p. 450.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MRBConstant.html">MRB Constant</a>

%p MRB:= Sum((-1)^k*(k^(1/k)-1),k=1..infinity):

%p V:= evalf[150](MRB):

%p subs(`...`=NULL, numtheory:-cfrac(V, 100, 'quotients')); # _Robert Israel_, Jan 12 2015

%t m = NSum[(-1)^n*(n^(1/n) - 1), {n, 1, Infinity},

%t    WorkingPrecision -> 100, Method -> "AlternatingSigns"];

%t ContinuedFraction[m]

%o (PARI) contfrac(sumalt(x=1, (-1)^x*((x^(1/x))-1)) ) \\ _Michel Marcus_, Jan 12 2015

%Y Cf. A037077 (decimal expansion).

%K nonn,cofr,changed

%O 0,2

%A _Marvin Ray Burns_, Jan 11 2015