

A194469


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


3



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
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OFFSET

1,2


COMMENTS

Suppose that r and c are real numbers, that 0<c<1, and that s(n)=sum{<c+k*r><k*r> : 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.


LINKS

Table of n, a(n) for n=1..36.


MATHEMATICA

(See A194368.)


CROSSREFS

Cf. A194368.
Sequence in context: A331085 A132791 A125297 * A143072 A089648 A062861
Adjacent sequences: A194466 A194467 A194468 * A194470 A194471 A194472


KEYWORD

nonn


AUTHOR

Clark Kimberling, Aug 24 2011


STATUS

approved



