A001955 Beatty sequence of 1 + 1/sqrt(11). (Formerly M0615 N0225)

1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 22, 23, 24, 26, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 61, 62, 63, 65, 66, 67, 68, 70, 71, 72, 74, 75, 76, 78, 79, 80, 81, 83, 84, 85, 87, 88

Offset

1,2

Comments

From R. J. Mathar, Feb 12 2011: (Start)

The value of 1+1/sqrt(11) = 1.30151134457.. is close to (sqrt(13)-1)/2 = 1.3027756377..., so the early terms of the sequence are similar to A184480.

According to the Fraenkel article, the complementary sequence is defined by floor(n*(1+sqrt(11)). (End)

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Ian G. Connell, A generalization of Wythoff's game, Canad. Math. Bull. 2 (1959) 181-190

A. S. Fraenkel, How to beat your Wythoff games' opponent on three fronts, Amer. Math. Monthly, 89 (1982), 353-361.

Index entries for sequences related to Beatty sequences

Maple

A001955 := proc(n) local x ; x := 1+1/sqrt(11) ; floor(n*x) ; end proc:
# for the complementary sequence
A001955compl := proc(n) local x ; x := 1+sqrt(11) ; floor(n*x) ; end proc:
seq(A001955(n), n=1..100) ; # R. J. Mathar, Feb 12 2011

Mathematica

Table[Floor[n*(1 + 1/Sqrt[11])], {n, 1, 65}]

Crossrefs

Sequence in context: A045671 A276341 A098572 * A184480 A194375 A188222

Adjacent sequences: A001952 A001953 A001954 * A001956 A001957 A001958

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Robert G. Wilson v, Nov 02 2000

Status

approved