OFFSET
1,1
COMMENTS
Determine the continued fraction convergents to e^(-G) = .561459484...; the first few being 1/1, 1/2, 4/7, 5/9, 9/16, 32/57...(check: 32/57 = .561403508...). Pick a convergent, a/b say 5/9. Then through (a+b) = n = 14, 5 of those integers are in the upper Beatty pair set: 2, 5, 8, 11, 13; while 9 terms are in the lower Beatty pair set, being 1, 3, 4, 6, 7, 9, 10, 12, 14. Since the upper Beatty pair set is derived from (k+1) and the lower from (k+1)/k, the ratio of upper to lower converges to k = 1.789107241...= e^G.
FORMULA
a(n) = floor (n*(k+1)) where k = 1.781072417...= e^G, G = Euler's gamma constant, .577215664901...
EXAMPLE
a(7) = 19 since floor(n*2.7810724...) = 19.
MATHEMATICA
Table[ Floor[ n*(E^EulerGamma + 1)], {n, 65}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Apr 04 2004
EXTENSIONS
More terms from Robert G. Wilson v, Apr 05 2004
STATUS
approved