cp's OEIS Frontend

A248660 Simple continued fraction expansion of the constant defined in A037077.

%I A248660 #37 Feb 16 2025 08:33:23
%S A248660 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 A248660 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 A248660 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 A248660 Simple continued fraction expansion of the constant defined in A037077.
%C A248660 A037077 is sometimes called the MRB constant.
%D A248660 Steven R. Finch, Mathematical Constants, Cambridge, 2003, p. 450.
%H A248660 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MRBConstant.html">MRB Constant</a>
%p A248660 MRB:= Sum((-1)^k*(k^(1/k)-1),k=1..infinity):
%p A248660 V:= evalf[150](MRB):
%p A248660 subs(`...`=NULL, numtheory:-cfrac(V, 100, 'quotients')); # _Robert Israel_, Jan 12 2015
%t A248660 m = NSum[(-1)^n*(n^(1/n) - 1), {n, 1, Infinity},
%t A248660    WorkingPrecision -> 100, Method -> "AlternatingSigns"];
%t A248660 ContinuedFraction[m]
%o A248660 (PARI) contfrac(sumalt(x=1, (-1)^x*((x^(1/x))-1)) ) \\ _Michel Marcus_, Jan 12 2015
%Y A248660 Cf. A037077 (decimal expansion).
%K A248660 nonn,cofr
%O A248660 0,2
%A A248660 _Marvin Ray Burns_, Jan 11 2015