cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A105960 Smallest integer q >= 1 such that difference between q*sqrt(2) and the nearest integer is <= 1/n.

Original entry on oeis.org

1, 2, 2, 2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29
Offset: 2

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Author

N. J. A. Sloane, Jun 18 2005

Keywords

Comments

Theorem 1 in Cassels says given real numbers x and Q>1, there is an integer q such that 0 < q < Q and the difference between qx and the nearest integer is <= 1/Q. This sequence arises from taking x = sqrt(2) and Q = n = 2,3,4,...

References

  • J. W. S. Cassels, An Introduction to Diophantine Approximation, Cambridge, 1957.

Crossrefs

Cf. Pell numbers A000129; A108688, A108689.

Programs

  • Maple
    Digits:=200; M1:=200; th:=x->abs(x-round(x)); f:=proc(x) local Q,q,t1,x1; t1:=[]; for Q from 2 to M1 do x1:=evalf(1/Q); q:=1; while th(q*x) > x1 do q:=q+1; od; t1:=[op(t1),q]; od; t1; end; f(evalf(sqrt(2)));
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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