A183142 -id:A183142 - cp's OEIS frontend

A183143 [1/r]+[2/r]+...+[n/r], where r=sqrt(3) and []=floor.

0, 1, 2, 4, 6, 9, 13, 17, 22, 27, 33, 39, 46, 54, 62, 71, 80, 90, 100, 111, 123, 135, 148, 161, 175, 190, 205, 221, 237, 254, 271, 289, 308, 327, 347, 367, 388, 409, 431, 454, 477, 501, 525, 550, 575, 601, 628, 655, 683, 711, 740, 770, 800, 831

Offset: 1

Clark Kimberling, Dec 26 2010

A183143 + A183144 = A000217 (the triangular numbers).

Cf. A183142, A183144, A183136.

A183143 := proc(n)
    local r;
    r := sqrt(3) ;
    add( floor(i/r),i=1..n) ;
end proc:
seq( A183143(n),n=1..200) ; # R. J. Mathar, Aug 28 2025

Accumulate[Floor[Range[60]/Sqrt[3]]] (* Harvey P. Dale, Sep 10 2019 *)

default(realprecision,100); r=sqrt(3); for(n=1,99,print1(sum(k=1,n,floor(k/r)),", "))

[1/r]+[2/r]+...+[n/r], where r=sqrt(3) and []=floor.

A183144 [1/s]+[2/s]+...+[n/s], where s=(3+sqrt(3))/2, []=floor.

Original entry on oeis.org

0, 0, 1, 2, 4, 6, 8, 11, 14, 18, 22, 27, 32, 37, 43, 49, 56, 63, 71, 79, 87, 96, 105, 115, 125, 135, 146, 157, 169, 181, 194, 207, 220, 234, 248, 263, 278, 294, 310, 326, 343, 360, 378, 396, 415, 434, 453, 473, 493, 514, 535, 556, 578, 600, 623

Offset: 1

Clark Kimberling, Dec 26 2010

nonn

A183143 + A183144 = A000217 (the triangular numbers).

Cf. A183142, A183143.

With[{c=(3+Sqrt[3])/2},Accumulate[Floor[Range[60]/c]]] (* Harvey P. Dale, Mar 30 2018 *)

[1/s]+[2/s]+...+[n/s], where s=(3+sqrt(3))/2, []=floor.

cp's OEIS Frontend

A183143 [1/r]+[2/r]+...+[n/r], where r=sqrt(3) and []=floor.

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