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

%I A217793 #12 Feb 16 2025 08:33:18
%S A217793 0,7,13,0,11,24,34,41,0,15,32,44,58,74,85,0,23,48,75,93,113,135,159,
%T A217793 185,202,221,0,27,56,87,107,142,166,192,220,237,269,290,313,0,35,72,
%U A217793 111,152,178,206,253,285,319,355,376,416,458,485,514,545,0,39,80
%N A217793 Erdős-Turán Golomb rulers, triangle read by rows.
%H A217793 Reinhard Zumkeller, <a href="/A217793/b217793.txt">Rows n = 1..60 of triangle, flattened</a>
%H A217793 P. Erdős and P. Turán, <a href="http://www.renyi.hu/~p_erdos/1941-01.pdf">On a problem of Sidon in additive number theory, and on some related problems</a>, J. Lond. Math. Soc. 16 (1941), 212-215.
%H A217793 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GolombRuler.html">Golomb Ruler.</a>
%H A217793 Wikipedia, <a href="http://en.wikipedia.org/wiki/Golomb_ruler">Golomb ruler</a>
%H A217793 <a href="/index/Go#Golomb">Index entries for sequences related to Golomb rulers</a>
%F A217793 T(n,k) = 2*p*k + k^2 mod p with p = n-th odd prime and 0 <= k < p.
%e A217793 First rows:
%e A217793 .  1  0,7,13
%e A217793 .  2  0,11,24,34,41
%e A217793 .  3  0,15,32,44,58,74,85
%e A217793 .  4  0,23,48,75,93,113,135,159,185,202,221
%e A217793 .  5  0,27,56,87,107,142,166,192,220,237,269,290,313
%e A217793 .  6  0,35,72,111,152,178,206,253,285,319,355,376,416,458,485,514,545 .
%o A217793 (Haskell)
%o A217793 a217793 n k = a217793_tabf !! (n-1) !! k
%o A217793 a217793_row n = a217793_tabf !! (n-1)
%o A217793 a217793_tabf =
%o A217793    map (\p -> [2*p*k + k^2 `mod` p | k <- [0..p-1]]) a065091_list
%Y A217793 Cf. A065091 (row lengths).
%K A217793 nonn,tabf
%O A217793 1,2
%A A217793 _Reinhard Zumkeller_, Mar 25 2013