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%I #6 Sep 13 2016 14:33:30
%S 1,1,1,1,4,4,1,1,4,2,2,4,1,1,4,9,5,3,3,5,9,4,1,1,4,9,3,12,10,10,12,3,
%T 9,4,1,1,4,9,16,8,2,15,13,13,15,2,8,16,9,4,1,1,4,9,16,6,17,11,7,5,5,7,
%U 11,17,6,16,9,4,1,1,4,9,16,2,13,3,18,12,8,6,6,8,12,18,3,13,2,16,9,4,1
%N Irregular triangle by rows, squares mod primes; 1<=k<=n.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Quadratic_reciprocity">Quadratic reciprocity</a>.
%F Triangle read by rows n-th row = the first p(n) - 1 terms of k^2 mod p(n) such that the next term 0 = and the cycle repeats. The 0 term and repeating cycle are not included in the triangle. 1<=k<=n.
%e First few rows of the triangle =
%e 1;
%e 1, 1
%e 1, 4, 4, 1;
%e 1, 4, 2, 2, 4, 1;
%e 1, 4, 9, 5, 3, 3, 5, 9, 4, 1;
%e 1, 4, 9, 3, 12, 10, 10, 12, 3, 9, 4, 1;
%e ...
%e Row 3 = (1, 4, 4, 1) = the truncated cycle of (1, 4, 4, 1, 0, 1, 4, 4, 1, 0,...) = squares of (1, 2, 3,...) mod 5
%t Table[ Mod[k^2, Prime@n], {n, 10}, {k, Prime@n - 1}] // Flatten (* _Robert G. Wilson v_, Aug 31 2008 *)
%Y Cf. A000040.
%K nonn,tabf
%O 1,5
%A _Gary W. Adamson_, Aug 02 2008
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