A183140 -id:A183140 - cp's OEIS frontend

A183138 a(n) = floor(n/(2+sqrt(2))).

0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20

Offset: 1

Clark Kimberling, Dec 26 2010

nonn

A083051(n) = 2*n+1 + floor(n*sqrt(2)) is the location of the least k for which a(k)=n.

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A183140. Beatty sequence of A268682.

[Floor(n/(2+Sqrt(2))): n in [1..100]]; // G. C. Greubel, Apr 10 2018

With[{c=2+Sqrt[2]},Table[Floor[n/c],{n,80}]] (* Harvey P. Dale, Jun 21 2017 *)

for(n=1,100, print1(floor(n/(2+sqrt(2))), ", ")) \\ G. C. Greubel Apr 10 2018

a(n) = floor(n/(2+sqrt(2))).

A183139 a(n) = [1/r]+[2/r]+...+[n/r], where r=sqrt(2) and []=floor.

Original entry on oeis.org

0, 1, 3, 5, 8, 12, 16, 21, 27, 34, 41, 49, 58, 67, 77, 88, 100, 112, 125, 139, 153, 168, 184, 200, 217, 235, 254, 273, 293, 314, 335, 357, 380, 404, 428, 453, 479, 505, 532, 560, 588, 617, 647, 678, 709, 741, 774, 807, 841, 876

Offset: 1

Clark Kimberling, Dec 26 2010

nonn

A183139 + A183140 = A000217 (the triangular numbers).

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A183139, A183140, A000217.

[(&+[Floor(k/Sqrt(2)):k in [1..n]]): n in [1..100]]; // G. C. Greubel, Apr 10 2018

Accumulate[Floor[Range[100]/(Sqrt[2])]] (* G. C. Greubel, Apr 10 2018 *)

for(n=1, 100, print1(sum(k=1,n, floor(k/sqrt(2))), ", ")) \\ G. C. Greubel, Apr 10 2018

a(n) = [1/r]+[2/r]+...+[n/r], where r=sqrt(2) and []=floor.

cp's OEIS Frontend

A183138 a(n) = floor(n/(2+sqrt(2))).

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