A194469 Values of m for which sqrt(m) is curbed by 1/2; see Comments for "curbed by".

1, 2, 4, 5, 6, 9, 10, 12, 16, 17, 18, 20, 25, 26, 30, 36, 37, 38, 39, 41, 42, 49, 50, 52, 54, 55, 56, 64, 65, 66, 68, 70, 72, 81, 82, 84

Offset: 1

Author

Clark Kimberling, Aug 24 2011

Keywords

• nonn

Comments

Suppose that r and c are real numbers, that 0- : 1<=k<=n}, where < > denotes fractional part. The inequalities s(n)<0, s(n)=0, s(n)>0 yield up to three sequences that partition the set of positive integers, as in the examples cited at A194368. If s(n)>=0 for every n>=1, we say that r is curbed by c. For r=sqrt(m), clearly r is curbed by 1/2 if m is a square. Conjecture: there are infinitely many nonsquare m for which sqrt(m) is curbed by 1/2, and there are infinitely many m for which sqrt(m) is not curbed by 1/2 (see A194470).

The terms shown here for A194469 are conjectured, based on examinations of s(n) for 1<=n<=B for various B>100.

Crossrefs

Cf. A194368.

Programs

Mathematica

(See A194368.)