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

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

Author

N. J. A. Sloane

Keywords

• nonn

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

Programs

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}]

Extensions

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