

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
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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.


LINKS

Table of n, a(n) for n=1..61.


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 A140101
Adjacent sequences: A093606 A093607 A093608 * A093610 A093611 A093612


KEYWORD

nonn


AUTHOR

Gary W. Adamson, Apr 04 2004


EXTENSIONS

More terms from Robert G. Wilson v, Apr 05 2004


STATUS

approved



