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A013942 Triangle of numbers T(n,k) = floor(2n/k), k=1..2n, read by rows. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A007739 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

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Last modified February 21 10:49 EST 2019. Contains 320372 sequences. (Running on oeis4.)