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

1,2

Comments

A037077 is sometimes called the MRB constant.

References

S. R. Finch, Mathematical Constants, Cambridge, 2003, p. 450.

Links

Table of n, a(n) for n=1..99.

Eric Weisstein's World of Mathematics, MRB Constant

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]

Prog

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

Crossrefs

Sequence in context: A108245 A228789 A221715 * A141620 A195140 A049829

Adjacent sequences: A248657 A248658 A248659 * A248661 A248662 A248663

Keyword

nonn,cofr

Author

Marvin Ray Burns, Jan 11 2015

Status

approved