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A228179 Irregular table where the n-th row consists of the square roots of 1 in Z_n.

%I A228179 #41 Oct 26 2022 20:52:33
%S A228179 1,1,2,1,3,1,4,1,5,1,6,1,3,5,7,1,8,1,9,1,10,1,5,7,11,1,12,1,13,1,4,11,
%T A228179 14,1,7,9,15,1,16,1,17,1,18,1,9,11,19,1,8,13,20,1,21,1,22,1,5,7,11,13,
%U A228179 17,19,23,1,24,1,25,1,26,1,13,15,27,1,28,1,11
%N A228179 Irregular table where the n-th row consists of the square roots of 1 in Z_n.
%C A228179 Each 1 starts a new row.
%C A228179 This is a subsequence of A020652.
%C A228179 Row n has A060594(n) entries.
%C A228179 Each row forms a subgroup of the multiplicative group of units of Z_n.
%H A228179 Alois P. Heinz, <a href="/A228179/b228179.txt">Rows n = 2..2000 of irregular triangle, flattened</a>
%e A228179 The table starts out as follows:
%e A228179   1
%e A228179   1 2
%e A228179   1 3
%e A228179   1 4
%e A228179   1 5
%e A228179   1 6
%e A228179   1 3 5 7
%e A228179   1 8
%e A228179   1 9
%e A228179   1 10
%e A228179   1 5 7 11
%e A228179   ...
%p A228179 T:= n-> seq(`if`(k&^2 mod n=1, k, NULL), k=1..n-1):
%p A228179 seq(T(n), n=2..50);  # _Alois P. Heinz_, Aug 20 2013
%t A228179 Flatten[Table[Position[Mod[Range[n]^2, n], 1], {n, 2, 50}]] (* _T. D. Noe_, Aug 20 2013 *)
%o A228179 (Sage) [[i for i in [1..k-1] if (i*i).mod(k)==1] for k in [2..n]] #changing n gives you the table up to the n-th row.
%o A228179 (Python)
%o A228179 from itertools import chain, count, islice
%o A228179 from sympy.ntheory import sqrt_mod_iter
%o A228179 def A228179_gen(): # generator of terms
%o A228179     return chain.from_iterable((sorted(sqrt_mod_iter(1,n)) for n in count(2)))
%o A228179 A228179_list = list(islice(A228179_gen(),30)) # _Chai Wah Wu_, Oct 26 2022
%Y A228179 Cf. A060594, A038566, A020652, A082568.
%Y A228179 Cf. A070667 (second column), A358016 (second-last column).
%Y A228179 Cf. A277776 (nontrivial square roots of 1).
%K A228179 nonn,easy,tabf
%O A228179 2,3
%A A228179 _Tom Edgar_, Aug 20 2013