A217793 Erdős-Turán Golomb rulers, triangle read by rows.

0, 7, 13, 0, 11, 24, 34, 41, 0, 15, 32, 44, 58, 74, 85, 0, 23, 48, 75, 93, 113, 135, 159, 185, 202, 221, 0, 27, 56, 87, 107, 142, 166, 192, 220, 237, 269, 290, 313, 0, 35, 72, 111, 152, 178, 206, 253, 285, 319, 355, 376, 416, 458, 485, 514, 545, 0, 39, 80

Offset

1,2

Links

Reinhard Zumkeller, Rows n = 1..60 of triangle, flattened

P. Erdős and P. Turán, On a problem of Sidon in additive number theory, and on some related problems, J. Lond. Math. Soc. 16 (1941), 212-215.

Eric Weisstein's World of Mathematics, Golomb Ruler.

Wikipedia, Golomb ruler

Index entries for sequences related to Golomb rulers

Formula

T(n,k) = 2*p*k + k^2 mod p with p = n-th odd prime and 0 <= k < p.

Example

First rows:
.  1  0,7,13
.  2  0,11,24,34,41
.  3  0,15,32,44,58,74,85
.  4  0,23,48,75,93,113,135,159,185,202,221
.  5  0,27,56,87,107,142,166,192,220,237,269,290,313
.  6  0,35,72,111,152,178,206,253,285,319,355,376,416,458,485,514,545 .

Prog

(Haskell)
a217793 n k = a217793_tabf !! (n-1) !! k
a217793_row n = a217793_tabf !! (n-1)
a217793_tabf =
   map (\p -> [2*p*k + k^2 `mod` p | k <- [0..p-1]]) a065091_list

Crossrefs

Cf. A065091 (row lengths).

Sequence in context: A157808 A354301 A225227 * A299472 A285642 A209189

Adjacent sequences: A217790 A217791 A217792 * A217794 A217795 A217796

Keyword

nonn,tabf

Author

Reinhard Zumkeller, Mar 25 2013

Status

approved