This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A213272 #25 May 27 2019 04:37:28 %S A213272 1,2,0,8,0,12,0,0,0,40,0,48,0,0,0,128,0,108,0,0,0,220,0,0,0,0,0,336,0 %N A213272 Costas arrays such that the terms in each row of the difference table are unique modulo n. %C A213272 Permutations of n elements such that each row in the difference table consists of pairwise distinct elements, even when taken modulo n (see example). %C A213272 For n<=29 the nonzero terms a(n) appear for n in A006093 (primes minus 1) and a(n)=A002618(n) (n*phi(n)); omitting the zeros we obtain A104039 (number of primitive roots modulo (p(n))^2, where p(n) is n-th prime). %C A213272 A002618(n) divides a(n) for all n, since (treating elements as integers modulo n) adding or subtracting a constant from each element or multiplying each element by an integer coprime to n preserves distinctness of all values modulo n. - _Charlie Neder_, May 26 2019 %H A213272 Scott Rickard, <a href="http://costasarrays.org/">costasarrays.org</a> (information and papers about Costas arrays). [broken link?] %H A213272 Wikipedia, <a href="https://en.wikipedia.org/wiki/Costas_array">Costas array</a>. %e A213272 The permutation (10, 9, 2, 8, 6, 1, 3, 7, 4, 5) corresponds to a Costas array: %e A213272 10 9 2 8 6 1 3 7 4 5 (Permutation: p(1), p(2), p(3), ..., p(n) ) %e A213272 -1 -7 6 -2 -5 2 4 -3 1 (step-1 differences: p(2)-p(1), p(3)-p(2), ... ) %e A213272 -8 -1 4 -7 -3 6 1 -2 (step-2 differences: p(3)-p(1), p(4)-p(2), ... ) %e A213272 -2 -3 -1 -5 1 3 2 (step-3 differences: p(4)-p(1), p(5)-p(2), ... ) %e A213272 -4 -8 1 -1 -2 4 ( etc. ) %e A213272 -9 -6 5 -4 -1 %e A213272 -7 -2 2 -3 %e A213272 -3 -5 3 %e A213272 -6 -4 %e A213272 -5 %e A213272 The values in each row are unique also modulo n=10: %e A213272 10 9 2 8 6 1 3 7 4 5 (Permutation: p(1), p(2), p(3), ..., p(n) ) %e A213272 9 3 6 8 5 2 4 7 1 (step-1 differences: p(2)-p(1), p(3)-p(2), ... ) %e A213272 2 9 4 3 7 6 1 8 (step-2 differences: p(3)-p(1), p(4)-p(2), ... ) %e A213272 8 7 9 5 1 3 2 (step-3 differences: p(4)-p(1), p(5)-p(2), ... ) %e A213272 6 2 1 9 8 4 ( etc. ) %e A213272 1 4 5 6 9 %e A213272 3 8 2 7 %e A213272 7 5 3 %e A213272 4 6 %e A213272 5 %Y A213272 Cf. A008404 (Costas arrays), A213270 (Costas arrays that are involutions), A213271 (Costas arrays that are derangements), A213338 (Costas arrays that are cyclic), A213339 (Costas arrays that are connected). %K A213272 nonn,hard,more %O A213272 1,2 %A A213272 _Joerg Arndt_, Jun 08 2012