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

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, 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, 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

Offset: 0

Author

Marvin Ray Burns, Jan 11 2015

Keywords

• nonn
• cofr

Comments

A037077 is sometimes called the MRB constant.

References

• Steven R. Finch, Mathematical Constants, Cambridge, 2003, p. 450.

Links

• Eric Weisstein's World of Mathematics, MRB Constant

Crossrefs

Cf. A037077 (decimal expansion).

Programs

Maple

MRB:= Sum((-1)^k*(k^(1/k)-1),k=1..infinity):
V:= evalf[150](MRB):
subs(`...`=NULL, numtheory:-cfrac(V, 100, 'quotients')); # Robert Israel, Jan 12 2015

Mathematica

m = NSum[(-1)^n*(n^(1/n) - 1), {n, 1, Infinity},
   WorkingPrecision -> 100, Method -> "AlternatingSigns"];
ContinuedFraction[m]

PARI

contfrac(sumalt(x=1, (-1)^x*((x^(1/x))-1)) ) \\ Michel Marcus, Jan 12 2015