Cahen’s constant

Whereas a simple additionPlanetmathPlanetmath of unit fractions with the terms of Sylvester’s sequenceMathworldPlanetmath as denominators gives as a result the integer 1, an alternating sum


(where ai is the ith term of Sylvester’s sequence) gives the transcendental numberMathworldPlanetmath known as Cahen’s constant (after Eugène Cahen) with an approximate decimal value of 0.643410546288338026182254307757564763286587860268239505987 (see A118227 in Sloane’s OEIS). Alternatively, we can express Cahen’s constant as


The recurrence relationMathworldPlanetmath bn+2=bn2bn+1+bn gives us the terms for the continued fractionMathworldPlanetmath representation of this constant:

Title Cahen’s constant
Canonical name CahensConstant
Date of creation 2013-03-22 16:24:04
Last modified on 2013-03-22 16:24:04
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 5
Author PrimeFan (13766)
Entry type Definition
Classification msc 11A55
Synonym Cahen constant