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