login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A093609
Upper Beatty sequence for e^G, G = Euler's gamma constant.
1
2, 5, 8, 11, 13, 16, 19, 22, 25, 27, 30, 33, 36, 38, 41, 44, 47, 50, 52, 55, 58, 61, 63, 66, 69, 72, 75, 77, 80, 83, 86, 88, 91, 94, 97, 100, 102, 105, 108, 111, 114, 116, 119, 122, 125, 127, 130, 133, 136, 139, 141, 144, 147, 150, 152, 155, 158, 161, 164, 166, 169
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
Beatty complement is A093610.
Sequence in context: A329924 A330112 A206911 * A249118 A292643 A376954
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Apr 04 2004
EXTENSIONS
More terms from Robert G. Wilson v, Apr 05 2004
STATUS
approved