A013942 Triangle of numbers T(n,k) = floor(2n/k), k=1..2n, read by rows.

2, 1, 4, 2, 1, 1, 6, 3, 2, 1, 1, 1, 8, 4, 2, 2, 1, 1, 1, 1, 10, 5, 3, 2, 2, 1, 1, 1, 1, 1, 12, 6, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 14, 7, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 16, 8, 5, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 18, 9, 6, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 20, 10, 6, 5, 4, 3

Offset

1,1

Comments

a(n) is also the leading term in period of continued fraction for n-th nonsquare.

Row A026741(n) contains n and all rows with a smaller row number do not contain n. - Reinhard Zumkeller, Jun 04 2013

Links

Reinhard Zumkeller, Rows n = 1..100 of table, flattened

Formula

T(n,k) = floor(2n/k), k=1,...,2n.

T(n,k) = [1/{sqrt(k+n^2)}], k=1,2,...,2n, {}=fractional part, []=floor.

Example

First four rows:
  2 1
  4 2 1 1
  6 3 2 1 1 1
  8 4 2 2 1 1 1 1
  ...

Mathematica

f[n_, h_]:=FractionalPart[(n^2+h)^(1/2)];
g[n_, h_]:=Floor[1/f[n, h]];
TableForm[Table[g[n, h], {n, 1, 13}, {h, 1, 2n}]]

Prog

(Haskell)
a013942 n k = a013942_tabf !! (n-1) !! (k-1)
a013942_row n = map (div (n * 2)) [1 .. 2 * n]
a013942_tabf = map a013942_row [1 ..]
-- Reinhard Zumkeller, Jun 04 2013
(PARI) T(n, k) = 2*n\k;
tabf(nn) = for (n=1, nn, for (k=1, 2*n, print1(T(n, k), ", ")); print()); \\ Michel Marcus, Sep 30 2016

Crossrefs

Cf. A010766.

Cf. A005843 (row lengths and left edge), A062550 (row sums).

Sequence in context: A330086 A290935 A031424 * A187816 A088423 A006839

Adjacent sequences: A013939 A013940 A013941 * A013943 A013944 A013945

Keyword

nonn,tabf,easy,nice

Author

Clark Kimberling

Extensions

Keyword tabl replaced by tabf and missing a(90)=1 inserted by Reinhard Zumkeller, Jun 04 2013

Status

approved