

A049473


Nearest integer to n/sqrt(2).


4



0, 1, 1, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 11, 11, 12, 13, 13, 14, 15, 16, 16, 17, 18, 18, 19, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 27, 28, 28, 29, 30, 30, 31, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 39, 40, 40, 41, 42, 42, 43, 44, 45, 45, 46, 47, 47
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OFFSET

0,4


COMMENTS

a(n) = floor(n*sqrt(2))  floor(n/sqrt(2)). Indeed, the equation {(nearest integer to n/r) = floor(nr)  floor(n/r) for all n>=0} has exactly two solutions: sqrt(2) and sqrt(2).  Clark Kimberling, Dec 18 2003
Let s(n) = zeta(3)  Sum_{k=1..n} 1/k^3. Conjecture: for n >=1, s(a(n)) < 1/n^2 < s(a(n)1), and the difference sequence of A049473 consists solely of 0's and 1, in positions given by the nonhomogeneous Beatty sequences A001954 and A001953, respectively.  Clark Kimberling, Oct 05 2014


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000


MATHEMATICA

Round[Range[0, 70]/Sqrt[2]] (* Harvey P. Dale, Feb 17 2015 *)


PROG

(PARI) a(n)=round(n/sqrt(2)) \\ Charles R Greathouse IV, Sep 02 2015
(MAGMA) [0] cat [Round(n/Sqrt(2)): n in [1..100]]; // G. C. Greubel, Jan 27 2018


CROSSREFS

Cf. A091087.
Sequence in context: A189730 A249569 A094500 * A154951 A095769 A080820
Adjacent sequences: A049470 A049471 A049472 * A049474 A049475 A049476


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


STATUS

approved



